{"id":25657,"date":"2022-04-05T11:50:32","date_gmt":"2022-04-05T06:20:32","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=25657"},"modified":"2022-04-07T11:46:50","modified_gmt":"2022-04-07T06:16:50","slug":"big-ideas-math-answers-grade-6-chapter-6","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6-chapter-6\/","title":{"rendered":"Big Ideas Math Answers Grade 6 Chapter 6 Equations"},"content":{"rendered":"<p><strong>Download Big Ideas Math Answers Grade 6 Chapter 6 Equations P<\/strong><strong style=\"font-size: 16px;\">df<\/strong><span style=\"font-size: 16px;\"> for free of cost. If you are browsing for various questions of equations, then here is the one-stop solution. Know the benefit of referring to Big Ideas Math Book 6th Grade Answer Key Chapter 6 Equations. You can learn the tips and simple methods to solve all the problems. With the below-given material, it acts as a guide to get better marks in the exam. Get a free step-by-step solution from this ultimate guide ie., <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6\/\">BIM 6th Grade Solutions<\/a> Ch 6 Equations. Check the below sections to get various details and information.<\/span><\/p>\n<h2>Big Ideas Math Book 6th Grade Answer Key Chapter 6 Equations<\/h2>\n<p>It is necessary for the candidates to understand the concept in maths. Concept is important than scoring marks in the exam. Therefore relate the questions with real-time problems and understand the concept in depth. With all the factors into consideration, <em><strong>BIM 6th Grade Answer Key or Equations Pdf<\/strong><\/em> is prepared. Click on the links in the next sections and start practicing the problems. Follow the various topics, Steam videos and Solved problems available in BIM Equations book and pdf.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Equations_STEAM_Video\/_Performance_Task\">Equations STEAM Video\/ Performance Task<\/a><\/li>\n<li><a href=\"#Equations_Getting_Ready_for_Chapter_6\">Equations Getting Ready for Chapter 6<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 1: Writing Equations in One Variable<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_6.1_Writing_Equations_in_One_Variable\">Lesson 6.1 Writing Equations in One Variable<\/a><\/li>\n<li><a href=\"#Writing_Equations_in_One_Variable_Homework_&amp;_Practice_6.1\">Writing Equations in One Variable Homework &amp; Practice 6.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Solving Equations Using Addition or Subtraction<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_6.2_Solving_Equations_Using_Addition_or_Subtraction\">Lesson 6.2 Solving Equations Using Addition or Subtraction<\/a><\/li>\n<li><a href=\"#Solving_Equations_Using_Addition_or_Subtraction_Homework_&amp;_Practice_6.2\">Solving Equations Using Addition or Subtraction Homework &amp; Practice 6.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Solving Equations Using Multiplication or Division<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_6.3_Solving_Equations_Using_Multiplication_or_Division\">Lesson 6.3 Solving Equations Using Multiplication or Division<\/a><\/li>\n<li><a href=\"#Solving_Equations_Using_Multiplication_or_Division_Homework_&amp;_Practice_6.3\">Solving Equations Using Multiplication or Division Homework &amp; Practice 6.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Writing Equations in Two Variables<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_6.4_Writing_Equations_in_Two_Variables\">Lesson 6.4 Writing Equations in Two Variables<\/a><\/li>\n<li><a href=\"#Writing_Equations_in_Two_Variables_Homework_&amp;_Practice_6.4\">Writing Equations in Two Variables Homework &amp; Practice 6.4<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 6 &#8211; Equations<\/strong><\/p>\n<ul>\n<li><a href=\"#Equations_Connecting_Concepts\">Equations Connecting Concepts<\/a><\/li>\n<li><a href=\"#Equations_Chapter_Review\">Equations Chapter Review<\/a><\/li>\n<li><a href=\"#Equations_Cumulative_Practice\">Equations Cumulative Practice<\/a><\/li>\n<li><a href=\"#Equations_Practice_Test\">Equations Practice Test<\/a><\/li>\n<\/ul>\n<h3><a id=\"Equations_STEAM_Video\/_Performance_Task\"><\/a>Equations STEAM Video\/ Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>Rock Climbing<br \/>\nEquations can be used to solve many different kinds of problems in real life, such as estimating the amount of time it will take to climb a rock wall. Can you think of any other real-life situations where equations are useful?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25667\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 1\" width=\"220\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-1.png 220w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-1-210x300.png 210w\" sizes=\"(max-width: 220px) 100vw, 220px\" \/><br \/>\nIn rock climbing, a pitch is a section of a climbing route between two anchor points. Watch the STEAM Video \u201cRock Climbing.\u201d\ue027en answer the following questions.<br \/>\n1. How can you use pitches to estimate the amount of time it will take to climb a rock wall?<br \/>\n2. Are there any other methods you could use to estimate the amount of time it will take to climb a rock wall? Explain.<br \/>\n3. You know two of the three pieces of information below. Explain how you can find the missing piece of information.<br \/>\nAverage climbing speed<br \/>\nHeight of rock wall<br \/>\nTime to complete climb<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Planning the Climb<br \/>\nAfter completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given information about two rock-climbing routes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 2\" width=\"261\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-2.png 261w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-2-236x300.png 236w\" sizes=\"(max-width: 261px) 100vw, 261px\" \/><br \/>\nRoute 1: 500 feet, 125 feet per pitch<br \/>\nRoute 2: 1200 feet, 8 pitch<br \/>\nYou will find the average speed of the climbers on Route 1 and the amount of time it takes to complete Route 2. Will the average speed of the climbers on Route 1 provide accurate predictions for the amount of time it takes to climb other routes? Explain why or why not.<\/p>\n<h3><a id=\"Equations_Getting_Ready_for_Chapter_6\"><\/a>Equations Getting Ready for Chapter 6<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p>Work with a partner. Every equation that has an unknown variable can be written as a question. Write a question that represents the equation. Then answer the question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 3\" width=\"547\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-3.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-3-300x116.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-52322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-3-300x116.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-3\" width=\"300\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-3-300x116.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-3.jpg 547w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Work with a partner. Write an equation that represents the question. Then answer the question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 4\" width=\"535\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-4.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-4-300x135.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-52323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-4-300x135.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-4\" width=\"300\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-4-300x135.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-4.jpg 535w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Vocabulary<\/strong><br \/>\nThe following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.<br \/>\nequation<br \/>\nindependent variable<br \/>\ninverse operations<br \/>\ndependent variable<br \/>\nequation in two variables.<\/p>\n<h3><a id=\"Lesson_6.1_Writing_Equations_in_One_Variable\"><\/a>Lesson 6.1 Writing Equations in One Variable<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing Equations<br \/>\nWork with a partner. Customers order sandwiches at a cafe from the menu board shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 1\" width=\"347\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-1.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-1-300x231.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><br \/>\na. The equation 6.75x =20.25 represents the purchase of one customer from the menu board. What does the equation tell you about the purchase? What cannot be determined from the equation?<br \/>\nb. The four customers in the table buy multiple sandwiches of the same type. For each customer, write an equation that represents the situation. Then determine how many sandwiches each customer buys. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25672\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 2\" width=\"633\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-2.png 633w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-2-300x77.png 300w\" sizes=\"(max-width: 633px) 100vw, 633px\" \/><br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 3\" width=\"187\" height=\"69\" \/><\/p>\n<p>An equation<br \/>\nis a mathematical sentence that uses an equal sign, =, to show that two expressions are equal.<br \/>\nExpressions<br \/>\n4 + 8<br \/>\nx + 8<br \/>\nEquations<br \/>\n4 + 8 = 12<br \/>\nx + 8 = 12<br \/>\nTo write a word sentence as an equation, look for key words or phrases such as is, the same as, or equals to determine where to place the equal sign.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Write the word sentence as an equation.<\/strong><br \/>\nQuestion 1.<br \/>\n9 less than a number be equals 2.<br \/>\nAnswer: 9-x=2<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase &#8220;less than&#8221; indicates -.<br \/>\nlet the number be x.<br \/>\n9 &#8211; x = 2<\/p>\n<p>Question 2.<br \/>\nThe product of a number g and 5 is 30.<br \/>\nAnswer: 5 \u00d7 g=30<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase &#8220;product&#8221; indicates &#8216;\u00d7&#8217;<br \/>\ng \u00d7 5 = 30<\/p>\n<p>Question 3.<br \/>\nA number k increased by 10 is the same as 24.<br \/>\nAnswer: k + 10 = 24<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase &#8220;increased&#8221; indicates &#8216;+&#8217;<br \/>\nThe equation is k + 10 = 24<\/p>\n<p>Question 4.<br \/>\nThe quotient of a number q and 4 is 12.<br \/>\nAnswer: q \u00f7 4 = 12<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase quotient indicates &#8216;\u00f7&#8217;<br \/>\nThe equation is q \u00f7 4 = 12<\/p>\n<p>Question 5.<br \/>\n2\\(\\frac{1}{2}\\) is the same as the sum of a number w and \\(\\frac{1}{2}\\).<br \/>\nAnswer: 2 \\(\\frac{1}{2}\\) = w + \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase sum indicates &#8216;+&#8217;<br \/>\nThe equation is 2 \\(\\frac{1}{2}\\) = w + \\(\\frac{1}{2}\\)<\/p>\n<p>Question 6.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nEach server decorates one table. Which equation can you use to find c?<br \/>\nAnswer: We can use the multiplication equation to find c.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow are expressions and equations different?<br \/>\nAnswer: An expression\u00a0is a number, a variable, or a combination of numbers and variables and operation symbols. An\u00a0equation\u00a0is made up of two\u00a0expressions\u00a0connected by an equal sign.<\/p>\n<p>Question 8.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Write \u201cboth\u201d equations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 4\" width=\"246\" height=\"163\" \/><br \/>\nAnswer: n-4=8<br \/>\n4&lt;8<\/p>\n<p>Question 9.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a word sentence for the equation 28 \u2212n= 5.<br \/>\nAnswer: 28 less than a number n is equals to 5.<\/p>\n<p>Question 10.<br \/>\n<strong>WRITING<\/strong><br \/>\nYou purchase x items for $4 each. Explain how the variable in the expression 4x and the variable in the equation 4x= 20 are similar. Explain how they are different.<br \/>\nAnswer:<br \/>\nYou purchase x items for $4 each<br \/>\n4x = 20<br \/>\nx = 20\/4<br \/>\nx = 5<\/p>\n<p>Question 11.<br \/>\nAfter four rounds, 74 teams are eliminated from a robotics competition. There are 18 teams remaining. Write and solve an equation to find the number of teams that started the competition.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nAfter four rounds, 74 teams are eliminated from a robotics competition. There are 18 teams remaining.<br \/>\nLet x be 74 teams<br \/>\nlet y be 18 teams<br \/>\nThe equation would be<br \/>\nx + y = 92<br \/>\n74 + 18 = 92<br \/>\nThus the total number of teams are 92.<\/p>\n<p>Question 12.<br \/>\nThe mass of the blue copper sulfate crystal is two-thirds the mass of the red fluorite crystal. Write an equation you can use to find the mass (in grams) of the blue copper sulfate crystal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 5\" width=\"115\" height=\"238\" \/><br \/>\nAnswer: blue copper sulfate crystal = 2\/3 (red fluorite crystal)<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou print photographs from a vacation. Find the number of photographs you can print for $3.60.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 6\" width=\"180\" height=\"157\" \/><br \/>\nAnswer: We can print 15 photographs for $3.60<\/p>\n<p>Explanation:<br \/>\nCost of each print = $0.24<br \/>\nThe total cost for photographs is $3.60<br \/>\n3.60\/0.24 = 15<br \/>\nThus We can print 15 photographs for $3.60<\/p>\n<h3><a id=\"Writing_Equations_in_One_Variable_Homework_&amp;_Practice_6.1\"><\/a>Writing Equations in One Variable Homework &amp; Practice 6.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Factor the expression using the GCF.<\/strong><br \/>\nQuestion 1.<br \/>\n6 + 27<br \/>\nAnswer: 3 (2 + 9)<\/p>\n<p>Explanation:<br \/>\nGiven the expression 6 + 27<br \/>\nTake 3 as the common factor<br \/>\n3(2 + 9)<\/p>\n<p>Question 2.<br \/>\n9w + 72<br \/>\nAnswer: 9(w + 8)<\/p>\n<p>Explanation:<br \/>\nGiven the expression 9w + 72<br \/>\nTake 9 as the common factor<br \/>\n9w + 72 = 9(w + 8)<\/p>\n<p>Question 3.<br \/>\n42 + 24n<br \/>\nAnswer: 6(7 + 4n)<\/p>\n<p>Explanation:<br \/>\nGiven the expression 42 + 24n<br \/>\nTake 6 as the common factor<br \/>\n42 + 24n = 6(7 + 4n)<\/p>\n<p>Question 4.<br \/>\n18h + 30k<br \/>\nAnswer: 6(3h + 5k)<\/p>\n<p>Explanation:<br \/>\nGiven the expression 18h + 30k<br \/>\nTake 6 as the common factor<br \/>\n18h + 30k = 6(3h + 5k)<\/p>\n<p>Question 5.<br \/>\nWhich number is not equal to 225%?<br \/>\nA. 2\\(\\frac{1}{4}\\)<br \/>\nB. \\(\\frac{9}{4}\\)<br \/>\nC. \\(\\frac{50}{40}\\)<br \/>\nD. \\(\\frac{45}{20}\\)<br \/>\nAnswer: C<br \/>\n225% is not equal to \\(\\frac{50}{40}\\)<\/p>\n<p><strong>Evaluate the expression when a = 7.<\/strong><br \/>\nQuestion 6.<br \/>\n6 + a<br \/>\nAnswer: 13<\/p>\n<p>Explanation:<br \/>\nGiven the expression 6 + a<br \/>\nwhere a = 7<br \/>\nSubstitute the value of a in the expression<br \/>\n6 + 7 = 13<\/p>\n<p>Question 7.<br \/>\na &#8211; 4<br \/>\nAnswer: 3<\/p>\n<p>Explanation:<br \/>\nGiven the expression a &#8211; 4<br \/>\nwhere a = 7<br \/>\nSubstitute the value of a in the expression<br \/>\na &#8211; 4<br \/>\n7 &#8211; 4 = 3<\/p>\n<p>Question 8.<br \/>\n4a<br \/>\nAnswer: 28<\/p>\n<p>Explanation:<br \/>\nGiven the expression 4a<br \/>\nwhere a = 7<br \/>\nSubstitute the value of a in the expression<br \/>\n4 \u00d7 7 = 28<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{35}{a}\\)<br \/>\nAnswer: 5<\/p>\n<p>Explanation:<br \/>\nGiven the expression \\(\\frac{35}{a}\\)<br \/>\nwhere a = 7<br \/>\nSubstitute the value of a in the expression<br \/>\n\\(\\frac{35}{7}\\) = 5<\/p>\n<p><strong>Find the perimeter of the rectangle.<\/strong><br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25677\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 7\" width=\"145\" height=\"126\" \/><br \/>\nAnswer:<br \/>\nl = 8 ft<br \/>\nArea = 40 sq ft<br \/>\nWe know that,<br \/>\nArea of rectangle = l \u00d7 w<br \/>\n40 sq. ft = 8 ft \u00d7 w<br \/>\nw = 40\/8 = 5 ft<br \/>\nThus the width of the above rectangle is 5 ft.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 8\" width=\"161\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nl = 13 cm<br \/>\nw = ?<br \/>\nA = 52 sq. cm<br \/>\nWe know that,<br \/>\nArea of rectangle = l \u00d7 w<br \/>\n52 sq. cm = 13 cm \u00d7 w<br \/>\nw = 52\/13<br \/>\nw = 4 cm<br \/>\nThus the width of the above rectangle is 4 cm.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 9\" width=\"101\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nA = 224 sq. miles<br \/>\nl = 14 miles<br \/>\nWe know that,<br \/>\nArea of rectangle = l \u00d7 w<br \/>\n224 sq. miles = 14 \u00d7 w<br \/>\nw = 224\/14<br \/>\nw = 16 miles<br \/>\nThus the width of the above figure is 16 miles.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>WRITING EQUATIONS<\/strong> A roast beef sandwich costs $6.75. A customer buys multiple roast beef sandwiches. Write an equation that represents the situation. Then determine how many sandwiches the customer buys. (See Exploration 1, p. 245.)<br \/>\nQuestion 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25680\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 10\" width=\"198\" height=\"80\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA roast beef sandwich costs $6.75.<br \/>\nAmount used for payment = $50.<br \/>\nChange Received = $16.25<br \/>\nThe total number of sandwich the customer buys = 5<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25681\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 11\" width=\"191\" height=\"79\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA roast beef sandwich costs $6.75.<br \/>\nAmount used for payment = $80.<br \/>\nChange Received = $19.25<br \/>\nAmount used for payment &#8211; Change Received<br \/>\n= $ 80 &#8211; $19.25<br \/>\n= $60.75<br \/>\n1 sandwich = $6.75<br \/>\nThe total number of sandwich the customer buys = 9<\/p>\n<p><strong>WRITING EQUATIONS<\/strong> Write the word sentence as an equation.<br \/>\nQuestion 15.<br \/>\nA number y decreased by 9 is 8.<br \/>\nAnswer: y &#8211; 9 = 8<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation form.<br \/>\ny &#8211; 9 = 8<\/p>\n<p>Question 16.<br \/>\nThe sum of a number x and 4 equals 12.<br \/>\nAnswer: x + 4 = 12<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation form.<br \/>\nx + 4 = 12<\/p>\n<p>Question 17.<br \/>\n9 times a number b is 36.<br \/>\nAnswer: 9b = 36<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation form.<br \/>\nThe phrase times indicates &#8216;\u00d7&#8217;<br \/>\nThe equation would be 9b = 36<\/p>\n<p>Question 18.<br \/>\nA number w divided by 5 equals 6.<br \/>\nAnswer: w \u00f7 5 = 6<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation form.<br \/>\nThe phrase divided by indicates &#8216;\u00f7&#8217;<br \/>\nThe equation would be w \u00f7 5 = 6<\/p>\n<p>Question 19.<br \/>\n54 equals 9 more than a number t.<br \/>\nAnswer: 54 = 9 + t<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation form.<br \/>\nThe phrase more than indicates &#8216;+&#8217;<br \/>\nThe equation would be 54 = 9 + t<\/p>\n<p>Question 20.<br \/>\n5 is one-fourth of a number c.<br \/>\nAnswer: 5 = 1\/4 c<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation form.<br \/>\nThe phrase of indicates &#8216;\u00d7&#8217;<br \/>\nThe equation would be 5 = 1\/4 c<\/p>\n<p>Question 21.<br \/>\n9.5 less than a number n equals 27.<br \/>\nAnswer: 9.5 &#8211; n = 27<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation form.<br \/>\nThe phrase less than indicates &#8216;-&#8216;<br \/>\nThe equation would be 9.5 &#8211; n = 27<\/p>\n<p>Question 22.<br \/>\n11\\(\\frac{3}{4}\\) is the quotient of a number y and 6\\(\\frac{1}{4}\\).<br \/>\nAnswer: 11\\(\\frac{3}{4}\\) = y \u00f7 6\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation form.<br \/>\nThe phrase quotient indicates &#8216;\u00f7&#8217;<br \/>\nThe equation would be 11\\(\\frac{3}{4}\\) = y \u00f7 6\\(\\frac{1}{4}\\)<\/p>\n<p>Question 23.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend writes the word sentence as an equation. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25682\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 12\" width=\"221\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nGiven the word sentence, 5 less than a number n is 12.<\/p>\n<p>Question 24.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nStudents and faculty raise $6042 for band uniforms. The faculty raised $1780. Write an equation you can use to find the amount a (in dollars) the students raised.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nStudents and faculty raise $6042 for band uniforms (x).<br \/>\nThe faculty raised $1780 (y)<br \/>\nThe students raised be z<br \/>\nz = x &#8211; y<br \/>\nz = 6042 &#8211; 1780<br \/>\nz = 4262<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou hit a golf ball 90 yards. It travels three-fourths of the distance to the hole. Write an equation you can use to find the distance d (in yards) from the tee to the hole.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25683\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 13\" width=\"267\" height=\"178\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou hit a golf ball 90 yards. It travels three-fourths of the distance to the hole.<br \/>\n3\/4 \u00d7 D = 90<br \/>\nD = 360\/3<br \/>\nD = 120<\/p>\n<p><strong>GEOMETRY<\/strong> Write an equation you can use to find the value of x.<br \/>\nQuestion 26.<br \/>\nPerimeter of triangle: 16 in.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 14\" width=\"121\" height=\"91\" \/><br \/>\nAnswer:<br \/>\nside of the triangle = x<br \/>\nPerimeter of triangle 16 in<br \/>\nP = a + b + c<br \/>\n16 in = x + x + x<br \/>\n3x = 16<br \/>\nx = 16\/3<br \/>\nx = 5.3<br \/>\nThus the side of the triangle is 5.3 inches.<\/p>\n<p>Question 27.<br \/>\nPerimeter of square: 30 mm<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25685\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 15\" width=\"84\" height=\"90\" \/><br \/>\nAnswer:<br \/>\n4x = 30<br \/>\nx = 30\/4<br \/>\nx = 7.5 mm<\/p>\n<p>Question 28.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas,6 sets of claves, and x djembe drums. Find the number of djembe drums you sold.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25686\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 16\" width=\"333\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-16.png 333w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-16-300x273.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><br \/>\nAnswer:<br \/>\nLet the price of maracas be m<br \/>\nLet the price of claves be c<br \/>\nLet the price of djembe drums be x<br \/>\nNumber of maracas = 12 sets<br \/>\nNumber of claves = 6 sets<br \/>\nNumber of djembe drums = xx<br \/>\nTotal earned amount = $326<br \/>\nThe equation would be<br \/>\n12m + 6c + dxx = 326<br \/>\nThe cost for 1 maracas is $14<br \/>\nFor 12 sets = 12 \u00d7 14 = $168<br \/>\nThe cost for 1 clave = $5<br \/>\nFor 6 sets = 6 \u00d7 5 = $30<br \/>\nThe cost for 1 djembe drums is $16<br \/>\nFor x sets = 16x<br \/>\n12m + 6c + dxx = 326<br \/>\n168 + 30 + 16x = 326<br \/>\n16x = 128<br \/>\nx = 128 \u00f7 16<br \/>\nx = 8<\/p>\n<p>Question 29.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nNeil Armstrong set foot on the Moon 109.4 hours after Apollo 11departed from the Kennedy Space Center. Apollo 11landed on the Moon about 6.6 hours before Armstrong\u2019s first step. How many hours did it take for Apollo 11 to reach the Moon?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nNeil Armstrong set foot on the Moon 109.4 hours after Apollo 11 departed from the Kennedy Space Center.<br \/>\nApollo 11landed on the Moon about 6.6 hours before Armstrong\u2019s first step.<br \/>\nTo find how many hours did it take for Apollo 11 to reach the Moon we have to subtract 6.6 hours from 109.4 hours<br \/>\n109.4 &#8211; 6.6 = 102.8 hours<br \/>\nThus it took 102.8 hours for Apollo 11 to reach the Moon.<\/p>\n<p>Question 30.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYou buy a basket of 24 strawberries. You eat them as you walk to the beach. It takes the same amount of time to walk each block. When you are halfway there, half of the berries are gone. After walking 3 more blocks, you still have 5 blocks to go. You reach the beach 28 minutes after you began. One-sixth of your strawberries are left.<br \/>\na. Is there enough information to find the time it takes to walk each block? Explain.<\/p>\n<p>Answer:<br \/>\nYes, you are given enough information to find the time to walk each block<br \/>\nTo find the total number of block you, add<br \/>\n3 + 5 + 8 = 16<br \/>\nAlso the time it takes to walk the 16 blocks is given 28 minutes.<\/p>\n<p>b. Is there enough information to find how many strawberries you ate while walking the last block? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 17\" width=\"224\" height=\"230\" \/><br \/>\nAnswer:<br \/>\nNo, there is not enough information to find how many strawberries ate while walking the last block.<br \/>\nYou are only given the amount of strawberries you started with 24 and what you have left (1\/6) with 5 blocks to go. Therefore you can only be given how many strawberries were eaten walking the last block.<\/p>\n<p>Question 31.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nFind a sales receipt from a store that shows the total price of the items and the total amount paid including sales tax.<br \/>\na. Write an equation you can use to find the sales tax rate r.<br \/>\nb. Can you use r to find the percent for the sales tax? Explain.<br \/>\nAnswer:<br \/>\nTotal amount paid = total price + (total price \u00d7 sales tax rate)<br \/>\nsample equation<br \/>\n14.20 = 13.27 + (13.27 \u00d7 0.07)<br \/>\nYes, you can use r to find the percent for the sales tax.<br \/>\nMultiplying r by 100 gives the percent for the sales tax.<\/p>\n<p>Question 32.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nA square is cut from a rectangle. The side length of the square is half of the unknown width w. The area of the shaded region is 84 square inches. Write an equation you can use to find the width (in inches).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25688\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-6.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations 6.1 18\" width=\"166\" height=\"104\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA square is cut from a rectangle. The side length of the square is half of the unknown width w.<br \/>\nThe area of the shaded region is 84 square inches.<br \/>\n84 square inches divided by 14 inches equals 6<br \/>\n84 divided by 14 = s<br \/>\n84 \u00f7 14 = s<\/p>\n<h3><a id=\"Lesson_6.2_Solving_Equations_Using_Addition_or_Subtraction\"><\/a>Lesson 6.2 Solving Equations Using Addition or Subtraction<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Solving an Equation Using a Tape Diagram<br \/>\nWork with a partner. A student solves an equation using the tape diagrams below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 1\" width=\"327\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-1.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-1-300x182.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\na. What equation did the student solve? What is the solution?<\/p>\n<p>Answer: x + 4 = 12<\/p>\n<p>Explanation:<br \/>\nBy seeing step 1 we can say that the equation for the above tape diagram x + 4 = 12<\/p>\n<p>b. Explain how the tape diagrams in Steps 2 and 3 relate to the equation and its solution.<br \/>\nAnswer:<br \/>\nBy seeing the steps 2 and 3 we can say<br \/>\n8 + 4 = 12<br \/>\nx + 4 = 12<br \/>\nx = 12 &#8211; 4<br \/>\nx = 8<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\nSolving an Equation Using a Model<br \/>\nWork with a partner.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-2.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 2\" width=\"416\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-2.png 416w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-2-300x131.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><br \/>\na. How are the two sides of an equation similar to a balanced scale?<br \/>\nb. When you add weight to one side of a balanced scale, what can you do to balance the scale? What if you subtract weight from one side of a balanced scale? How does this relate to solving an equation?<br \/>\nc. Use a model to solve x + 2 = 7. Describe how you can solve the equation algebraically.<br \/>\nAnswer:<br \/>\nx + 2 = 7<br \/>\nx = 7 &#8211; 2<br \/>\nx = 5<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 3\" width=\"186\" height=\"87\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Tell whether the given value is a solution of the equation.<\/strong><br \/>\nQuestion 1.<br \/>\na + 6 = 17; a = 9<br \/>\nAnswer: not a solution<\/p>\n<p>Explanation:<br \/>\nGiven the equation a + 6 = 17<br \/>\nwhen a = 9<br \/>\n9 + 6 = 17<br \/>\n15 \u2260 17<br \/>\nThus the equation is not a solution.<\/p>\n<p>Question 2.<br \/>\n9 &#8211; g = 5; g = 3<br \/>\nAnswer: not a solution<\/p>\n<p>Explanation:<br \/>\nGiven the equation 9 &#8211; g = 5<br \/>\nwhere g = 3<br \/>\n9 &#8211; 3 = 5<br \/>\n6 \u2260 5<br \/>\nThus the equation is not a solution.<\/p>\n<p>Question 3.<br \/>\n35 &#8211; 7n; n = 5<br \/>\nAnswer: solution<\/p>\n<p>Explanation:<br \/>\nGiven the equation 35 &#8211; 7n<br \/>\nwhere n = 5<br \/>\n35 &#8211; 7(5)<br \/>\n35 &#8211; 35 = 0<br \/>\nThus the equation is a solution.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{q}{2}\\) = 28; q = 14<br \/>\nAnswer: not a solution<\/p>\n<p>Explanation:<br \/>\nGiven the equation \\(\\frac{q}{2}\\) = 28<br \/>\nwhere q = 14<br \/>\n\\(\\frac{14}{2}\\) = 28<br \/>\n7 \u2260 28<br \/>\nThus the equation is not a solution.<\/p>\n<p>You can use inverse operations to solve equations. Inverse operations \u201cundo\u201d each other. Addition and subtraction are inverse operations.<\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 5.<br \/>\nk &#8211; 3 = 1<br \/>\nAnswer: k = 4<\/p>\n<p>Explanation:<br \/>\nGiven the equation k &#8211; 3 = 1<br \/>\nk = 1 + 3<br \/>\nk = 4<\/p>\n<p>Question 6.<br \/>\nn &#8211; 10 = 4<br \/>\nAnswer: n = 14<\/p>\n<p>Explanation:<br \/>\nGiven the equation n &#8211; 10 = 4<br \/>\nn = 4 + 10<br \/>\nn = 14<\/p>\n<p>Question 7.<br \/>\n15 = r &#8211; 6<br \/>\nAnswer: r = 21<\/p>\n<p>Explanation:<br \/>\nGiven the equation 15 = r &#8211; 6<br \/>\n15 + 6 = r<br \/>\nr = 21<\/p>\n<p>Question 8.<br \/>\ns + 8 = 17<br \/>\nAnswer: s = 9<\/p>\n<p>Explanation:<br \/>\nGiven the equation s + 8 = 17<br \/>\ns = 17 &#8211; 8<br \/>\ns = 9<\/p>\n<p>Question 9.<br \/>\n9 = y + 6<br \/>\nAnswer: y = 3<\/p>\n<p>Explanation:<br \/>\nGiven the equation 9 = y + 6<br \/>\n9 &#8211; 6 = y<br \/>\ny = 3<\/p>\n<p>Question 10.<br \/>\n13 + m = 20<br \/>\nAnswer: m = 7<\/p>\n<p>Explanation:<br \/>\nGiven the equation 13 + m = 20<br \/>\nm = 20 &#8211; 13<br \/>\nm = 7<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>CHECKING SOLUTIONS<\/strong> Tell whether the given value is a solution of the equation.<br \/>\nQuestion 11.<br \/>\nn + 8 = 42; n = 36<br \/>\nAnswer: not a solution<\/p>\n<p>Explanation:<br \/>\nGiven the equation n + 8 = 42<br \/>\nwhere n = 36<br \/>\n36 + 8 = 44<br \/>\n44 \u2260 42<br \/>\nThus the value is not a solution.<\/p>\n<p>Question 12.<br \/>\ng &#8211; 9 = 24; g = 35<br \/>\nAnswer: not a solution<\/p>\n<p>Explanation:<br \/>\nGiven the equation g &#8211; 9 = 24<br \/>\nwhere g = 35<br \/>\n35 &#8211; 9 = 24<br \/>\n26 \u2260 24<br \/>\nThus the value is not a solution.<\/p>\n<p><strong>SOLVING EQUATIONS<\/strong> Solve the equation. Check your solution.<br \/>\nQuestion 13.<br \/>\nx &#8211; 8 = 12<br \/>\nAnswer: 20<\/p>\n<p>Explanation:<br \/>\nGiven the equation x &#8211; 8 = 12<br \/>\nx = 12 + 8<br \/>\nx = 20<\/p>\n<p>Question 14.<br \/>\nb + 14 = 33<br \/>\nAnswer: 19<\/p>\n<p>Explanation:<br \/>\nGiven the equation b + 14 = 33<br \/>\nb = 33 &#8211; 14<br \/>\nb = 19<\/p>\n<p>Question 15.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhen solving x + 5 =16, why do you subtract 5 from the left side of the equation? Why do you subtract 5 from the right side of the equation?<br \/>\nAnswer:<br \/>\nTo solve the equation we have to subtract 5.<br \/>\nx + 5 = 16<br \/>\nx = 16 &#8211; 5<br \/>\nx = 11<\/p>\n<p>Question 16.<br \/>\n<strong>REASONING<\/strong><br \/>\nDo the equations have the same solution? Explain your reasoning.<br \/>\nx &#8211; 8 = 6<br \/>\nx &#8211; 6 = 8<br \/>\nAnswer:<br \/>\ni. x &#8211; 8 = 6<br \/>\nx = 6 + 8<br \/>\nx = 14<br \/>\nii. x &#8211; 6 = 8<br \/>\nx = 8 + 6<br \/>\nx = 14<br \/>\nYes both the equations has same solutions.<\/p>\n<p>Question 17.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nJust by looking at the equation x + 6 + 2x = 2x + 6 + 4, find the value of x. Explain your reasoning.<br \/>\nAnswer:<br \/>\nx + 6 + 2x = 2x + 6 + 4<br \/>\n3x + 6 = 2x + 10<br \/>\n3x &#8211; 2x = 10 &#8211; 6<br \/>\nx = 4<\/p>\n<p>Question 18.<br \/>\nAn emperor penguin is 45 inches tall. It is 24 inches taller than a rockhopper penguin. Write and solve an equation to find the height (in inches) of a rockhopper penguin. Is your answer reasonable? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25693\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-4.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 4\" width=\"186\" height=\"257\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nAn emperor penguin is 45 inches tall. It is 24 inches taller than a rockhopper penguin.<br \/>\n45 inches &#8211; 24 inches = 21 inches<br \/>\nThus the height of the rockhopper penguin is 21 inches.<\/p>\n<p>Question 19.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou get in an elevator and go up 2 floors and down8 floors before exiting. Then you get back in the elevator and go up 4 floors before exiting on the 12th floor. On what floors did you enter the elevator?<br \/>\nAnswer: The answer to your question is 14 floor<\/p>\n<p>Explanation:<br \/>\nTo solve this problem start from the end changing the sense if it says up, then consider the action as down, etc.<br \/>\nLast floor = 12<br \/>\nGo down 4 floors = 12 &#8211; 4 = 8<br \/>\nGo up 8 floors = 8 + 8 = 16<br \/>\nGo down 2 floors = 16 &#8211; 2 = 14<\/p>\n<h3><a id=\"Solving_Equations_Using_Addition_or_Subtraction_Homework_&amp;_Practice_6.2\"><\/a>Solving Equations Using Addition or Subtraction Homework &amp; Practice 6.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write the word sentence as an equation.<\/strong><br \/>\nQuestion 1.<br \/>\nTh sum of a number x and 9 is 15.<br \/>\nAnswer: x + 9 = 15<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase sum indicates &#8216;+&#8217;<br \/>\nThe equation would be x + 9 = 15<\/p>\n<p>Question 2.<br \/>\n12 less than a number m equals 20.<br \/>\nAnswer: 12 &#8211; m = 20<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase less than indicates &#8216;-&#8216;<br \/>\nThe equation would be 12 &#8211; m = 20<\/p>\n<p>Question 3.<br \/>\nThe product of a number d and 7 is 63.<br \/>\nAnswer: d7 = 63<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase product indicates &#8216;\u00d7&#8217;<br \/>\nThe equation would be d \u00d7 7 = 63<\/p>\n<p>Question 4.<br \/>\n18 divided by a number s equals 3.<br \/>\nAnswer: 18 \u00f7 s = 3<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase divided by indicates &#8216;\u00f7&#8217;<br \/>\nThe equation would be 18 \u00f7 s = 3<\/p>\n<p><strong>Divide. Write the answer in simplest form.<\/strong><br \/>\nQuestion 5.<br \/>\n\\(\\frac{1}{2}\\) \u00f7 \\(\\frac{1}{4}\\)<br \/>\nAnswer: 2<\/p>\n<p>Explanation:<br \/>\nDividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.<br \/>\nTake the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{4}{1}\\) = 2<\/p>\n<p>Question 6.<br \/>\n12 \u00f7 \\(\\frac{3}{8}\\)<br \/>\nAnswer: 32<\/p>\n<p>Explanation:<br \/>\nDividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.<br \/>\nTake the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes<br \/>\n12 \u00d7 \\(\\frac{8}{3}\\)<br \/>\n= 4 \u00d7 8<br \/>\n= 32<\/p>\n<p>Question 7.<br \/>\n8 \u00f7 \\(\\frac{4}{5}\\)<br \/>\nAnswer: 10<\/p>\n<p>Explanation:<br \/>\nDividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.<br \/>\nTake the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes<br \/>\n8 \u00d7 \\(\\frac{5}{4}\\)<br \/>\n= 2 \u00d7 5<br \/>\n= 10<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{7}{9}\\) \u00f7 \\(\\frac{3}{2}\\)<br \/>\nAnswer: \\(\\frac{14}{27}\\)<\/p>\n<p>Explanation:<br \/>\nDividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.<br \/>\nTake the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes<br \/>\n\\(\\frac{7}{9}\\) \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{14}{27}\\)<\/p>\n<p>Question 9.<br \/>\nWhich ratio is not equivalent to 72 : 18?<br \/>\nA. 36 : 9<br \/>\nB. 18 : 6<br \/>\nC. 4 : 1<br \/>\nD. 288 : 72<br \/>\nAnswer: B. 18 : 6<\/p>\n<p>Explanation:<br \/>\n72 : 18 = 36:9, 4 : 1, 288 : 72<br \/>\n18 : 6 is not equivalent to 72 : 18<br \/>\nThus the correct answer is option B.<\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 10.<br \/>\n(2 + 5<sup>2<\/sup>) \u00f7 3<br \/>\nAnswer: 9<\/p>\n<p>Explanation:<br \/>\nGiven the expression (2 + 5<sup>2<\/sup>) \u00f7 3<br \/>\n(2 + 25) \u00f7 3<br \/>\n27 \u00f7 3 = 9<\/p>\n<p>Question 11.<br \/>\n6 + 2<sup>3<\/sup> . 3 &#8211; 5<br \/>\nAnswer: 25<\/p>\n<p>Explanation:<br \/>\nGiven the expression 6 + 2<sup>3<\/sup> . 3 &#8211; 5<br \/>\n6 + 8 . 3 &#8211; 5<br \/>\n6 + 24 &#8211; 5<br \/>\n6 + 19<br \/>\n25<\/p>\n<p>Question 12.<br \/>\n4 . [3 + 3(20 &#8211; 4<sup>2<\/sup> &#8211; 2)]<br \/>\nAnswer: 36<\/p>\n<p>Explanation:<br \/>\nGiven the expression 4 . [3 + 3(20 &#8211; 4<sup>2<\/sup> &#8211; 2)]<br \/>\n4(3 + 3(20 &#8211; 16 &#8211; 2))<br \/>\n4(3 + 3(2))<br \/>\n4 (3 + 6)<br \/>\n4(9)<br \/>\n36<\/p>\n<p>Question 13.<br \/>\nFind the missing values in the ratio table. Then write the equivalent ratios.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25694\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-5.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 5\" width=\"178\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-5.jpg\" alt=\"Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-5\" width=\"178\" height=\"70\" \/><\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>CHOOSE TOOLS<\/strong> Use a model to solve the equation. (See Explorations 1 and 2, p. 251.)<br \/>\nQuestion 14.<br \/>\nn + 7 = 9<br \/>\nAnswer: n = 2<\/p>\n<p>Explanation:<br \/>\nn + 7 = 9<br \/>\nn = 9 &#8211; 7<br \/>\nn = 2<\/p>\n<p>Question 15.<br \/>\nt + 4 = 5<br \/>\nAnswer: t = 1<\/p>\n<p>Explanation:<br \/>\nt + 4 = 5<br \/>\nt = 5 &#8211; 4<br \/>\nt = 1<\/p>\n<p>Question 16.<br \/>\nc + 2 = 8<br \/>\nAnswer: c = 6<\/p>\n<p>Explanation:<br \/>\nc + 2 = 8<br \/>\nc = 8 &#8211; 2<br \/>\nc = 6<\/p>\n<p><strong>CHECKING SOLUTIONS<\/strong> Tell whether the given value is a solution of the equation.<br \/>\nQuestion 17.<br \/>\nx + 42 = 85; x = 43<br \/>\nAnswer: solution<\/p>\n<p>Explanation:<br \/>\nx + 42 = 85<br \/>\nSubstitute the value of x in the equation<br \/>\nx = 43<br \/>\n43 + 42 = 85<\/p>\n<p>Question 18.<br \/>\n8b = 48; b = 6<br \/>\nAnswer: solution<\/p>\n<p>Explanation:<br \/>\n8b = 48<br \/>\nSubstitute the value of b in the equation<br \/>\nb = 6<br \/>\n8(6) = 48<br \/>\n48 = 48<\/p>\n<p>Question 19.<br \/>\n19 &#8211; g = 7; g = 15<br \/>\nAnswer: not a solution<\/p>\n<p>Explanation:<br \/>\n19 &#8211; g = 7<br \/>\nSubstitute the value of g in the equation<br \/>\ng = 15<br \/>\n19 &#8211; 15 = 7<br \/>\n2 \u2260 7<br \/>\nThis is not a solution<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{m}{4}\\) = 16; m = 4<br \/>\nAnswer: not a solution<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{m}{4}\\) = 16<br \/>\nSubstitute the value of m in the equation<br \/>\n\\(\\frac{4}{4}\\) = 16<br \/>\n1 \u2260 16<br \/>\nThis is not a solution<\/p>\n<p>Question 21.<br \/>\nw + 23 = 41; w = 28<br \/>\nAnswer: not a solution<\/p>\n<p>Explanation:<br \/>\nw + 23 = 41<br \/>\nSubstitute the value of w in the equation<br \/>\n28 + 23 = 41<br \/>\n51 \u2260 41<br \/>\nThis is not a solution<\/p>\n<p>Question 22.<br \/>\ns &#8211; 68 = 11; s = 79<br \/>\nAnswer: solution<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\ns &#8211; 68 = 11<br \/>\nSubstitute the value of s in the equation<br \/>\ns = 79<br \/>\n79 &#8211; 68 = 11<br \/>\n11 = 11<br \/>\nThis is a solution<\/p>\n<p><strong>SOLVING EQUATIONS<\/strong> Solve the equation. Check your solution.<br \/>\nQuestion 23.<br \/>\ny &#8211; 7 = 3<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny &#8211; 7 = 3<br \/>\ny = 3 + 7<br \/>\ny = 10<\/p>\n<p>Question 24.<br \/>\nz &#8211; 3 = 13<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nz &#8211; 3 = 13<br \/>\nz = 13 +3<br \/>\nz = 16<\/p>\n<p>Question 25.<br \/>\n8 = r &#8211; 14<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n8 = r &#8211; 14<br \/>\nr = 8 + 14<br \/>\nr = 22<\/p>\n<p>Question 26.<br \/>\np + 5 = 8<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\np + 5 = 8<br \/>\np = 8 &#8211; 5<br \/>\np = 3<\/p>\n<p>Question 27.<br \/>\nk + 6 = 18<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nk + 6 = 18<br \/>\nk = 18 &#8211; 6<br \/>\nk = 12<\/p>\n<p>Question 28.<br \/>\n64 = h + 30<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n64 = h + 30<br \/>\nh = 64 &#8211; 30<br \/>\nh = 34<\/p>\n<p>Question 29.<br \/>\nf &#8211; 27 = 19<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nf &#8211; 27 = 19<br \/>\nf = 19 +27<br \/>\nf = 46<\/p>\n<p>Question 30.<br \/>\n25 = q + 14<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n25 = q + 14<br \/>\nq = 25 &#8211; 14<br \/>\nq = 11<\/p>\n<p>Question 31.<br \/>\n\\(\\frac{3}{4}\\) = j &#8211; \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n\\(\\frac{3}{4}\\) = j &#8211; \\(\\frac{1}{2}\\)<br \/>\n\\(\\frac{3}{4}\\) + \\(\\frac{1}{2}\\) = j<br \/>\nj = 1 \\(\\frac{1}{4}\\)<\/p>\n<p>Question 32.<br \/>\nx + \\(\\frac{2}{3}\\) = \\(\\frac{9}{10}\\)<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nx + \\(\\frac{2}{3}\\) = \\(\\frac{9}{10}\\)<br \/>\nx = \\(\\frac{9}{10}\\) &#8211; \\(\\frac{2}{3}\\)<br \/>\nx = \\(\\frac{7}{30}\\)<\/p>\n<p>Question 33.<br \/>\n1.2 = m &#8211; 2.5<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n1.2 = m &#8211; 2.5<br \/>\nm = 1.2 + 2.5<br \/>\nm = 3.7<\/p>\n<p>Question 34.<br \/>\na + 5.5 = 17.3<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\na + 5.5 = 17.3<br \/>\na = 17.3 &#8211; 5.5<br \/>\na = 11.8<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong> Your friend solves the equation. Is your friend correct? Explain your reasoning.<br \/>\nQuestion 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25695\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-6.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 6\" width=\"113\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nx + 7 = 13<br \/>\nx = 13 &#8211; 7<br \/>\nx = 4<br \/>\nYour friend is incorrect<\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25696\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-7.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 7\" width=\"162\" height=\"108\" \/><br \/>\nAnswer:<br \/>\n34 = y &#8211; 12<br \/>\ny &#8211; 12 = 34<br \/>\ny = 34 + 12<br \/>\ny = 46<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe main span of the Sunshine SkywayBridge is 366 meters long. The bridge\u2019s main span is 30 meters shorter than the main span of the Dames Point Bridge. Write and solve an equation to find the length (in meters) of the main span of the Dames Point Bridge.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-8.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 8\" width=\"285\" height=\"171\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe main span of the Sunshine SkywayBridge is 366 meters long.<br \/>\nThe bridge\u2019s main span is 30 meters shorter than the main span of the Dames Point Bridge.<br \/>\n336 &#8211; 30 = 306<br \/>\nLet the main span of the Sunshine SkywayBridge be x<br \/>\nLet the main span of the Dames Point Bridge be y<br \/>\nx &#8211; y = 306<\/p>\n<p>Question 38.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA park has 22 elm trees. Elm leaf beetles have been attacking the trees. After removing several of the diseased trees, there are 13 healthy elm trees left. Write and solve an equation to find the number of elm trees that were removed.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA park has 22 elm trees. Elm leaf beetles have been attacking the trees.<br \/>\nAfter removing several of the diseased trees, there are 13 healthy elm trees left.<br \/>\nx &#8211; y = 9<br \/>\n22 &#8211; 13 = 9<br \/>\nThus the number of trees removed 9.<\/p>\n<p>Question 39.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe area of Jamaica is 6460 square miles less than the area of Haiti. Find the area (in square miles) of Haiti.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25698\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-9.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 9\" width=\"380\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-9.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-9-300x139.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe area of Jamaica is 6460 square miles less than the area of Haiti.<br \/>\nY = X &#8211; 6460<br \/>\nY = Haiti<br \/>\nX = area of Jamaica<\/p>\n<p>Question 40.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe solution of the equation x+ 3 = 12 is shown. Explain each step. Use a property, if possible.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-10.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 10\" width=\"345\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-10.png 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-10-300x110.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><br \/>\nAnswer:<br \/>\nThe sum of a number x and 3 is 12<br \/>\nx + 3 = 12<br \/>\nx = 12 &#8211; 3<br \/>\nx = 9<\/p>\n<p><strong>WRITING EQUATIONS<\/strong> Write the word sentence as an equation. Then solve the equation.<br \/>\nQuestion 41.<br \/>\n13 subtracted from a number w is 15.<br \/>\nAnswer: w &#8211; 13 = 15<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase subtracted indicates &#8216;-&#8216;<br \/>\nThe equation would be w &#8211; 13 = 15<\/p>\n<p>Question 42.<br \/>\nA number k increased by 7 is 34.<br \/>\nAnswer: K + 7 = 34<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase increased indicates &#8216;+&#8217;<br \/>\nThe equation would be K + 7 = 34<\/p>\n<p>Question 43.<br \/>\n9 is the difference of a number n and 7.<br \/>\nAnswer: n &#8211; 7 = 9<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase difference indicates &#8216;-&#8216;<br \/>\nThe equation would be n &#8211; 7 = 9<\/p>\n<p>Question 44.<br \/>\n93 is the sum of a number g and 58.<br \/>\nAnswer: g + 58 = 93<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase sum indicates &#8216;+&#8217;<br \/>\nThe equation would be g + 58 = 93<\/p>\n<p>Question 45.<br \/>\n11 more than a number k equals 29.<br \/>\nAnswer: 11 + k = 29<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase more than indicates &#8216;+&#8217;<br \/>\nThe equation would be 11 + k = 29<\/p>\n<p>Question 46.<br \/>\nA number p decreased by 19 is 6.<br \/>\nAnswer: p &#8211; 19 = 6<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase decreased indicates &#8216;-&#8216;<br \/>\nThe equation would be p &#8211; 19 = 6<\/p>\n<p>Question 47.<br \/>\n46 is the total of 18 and a number d.<br \/>\nAnswer: 18 + d = 46<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase total indicates &#8216;+&#8217;<br \/>\nThe equation would be 18 + d = 46<\/p>\n<p>Question 48.<br \/>\n84 is 99 fewer than a number c.<br \/>\nAnswer: 84 = 99 &#8211; c<\/p>\n<p>Explanation:<br \/>\nWe have to write the equation for the word sentence<br \/>\nThe phrase fewer than indicates &#8216;-&#8216;<br \/>\nThe equation would be 84 = 99 &#8211; c<\/p>\n<p><strong>SOLVING EQUATIONS<\/strong> Solve the equation. Check your solution.<br \/>\nQuestion 49.<br \/>\nb + 7 + 12 = 30<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nb + 7 + 12 = 30<br \/>\nb = 30 &#8211; 19<br \/>\nb = 11<\/p>\n<p>Question 50.<br \/>\ny + 4 \u2212 1 = 18<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny + 4 \u2212 1 = 18<br \/>\ny + 3 = 18<br \/>\ny = 18 &#8211; 3<br \/>\ny = 15<\/p>\n<p>Question 51.<br \/>\nm + 18 + 23 = 71<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nm + 18 + 23 = 71<br \/>\nm + 41 = 71<br \/>\nm = 71 &#8211; 41<br \/>\nm = 30<\/p>\n<p>Question 52.<br \/>\nv \u2212 7 = 9 + 12<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nv \u2212 7 = 9 + 12<br \/>\nv &#8211; 7 = 21<br \/>\nv = 21 + 7<br \/>\nv = 28<\/p>\n<p>Question 53.<br \/>\n5 + 44 = 2 + r<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n5 + 44 = 2 + r<br \/>\n49 = 2 + r<br \/>\nr = 49 &#8211; 2<br \/>\nr = 47<\/p>\n<p>Question 54.<br \/>\n22 + 15 = d\u2212 17<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n22 + 15 = d\u2212 17<br \/>\n37 = d &#8211; 17<br \/>\nd = 37 + 17<br \/>\nd = 54<\/p>\n<p><strong>GEOMETRY<\/strong> Solve for x.<br \/>\nQuestion 55.<br \/>\nPerimeter = 48 ft<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-11.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 11\" width=\"102\" height=\"112\" \/><br \/>\nAnswer:<br \/>\nP = a + b + c<br \/>\n48 ft = x + 20 + 12<br \/>\nx = 48 &#8211; 32<br \/>\nx = 16 ft<\/p>\n<p>Question 56.<br \/>\nPerimeter = 132 in.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25701\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-12.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 12\" width=\"155\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nP = a + b + c + d<br \/>\n132 = 34 + 16 + 34 + x<br \/>\n132 &#8211; 84 = x<br \/>\nx = 50 in<\/p>\n<p>Question 57.<br \/>\nPerimeter = 93 ft<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25702\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-13.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 13\" width=\"150\" height=\"102\" \/><br \/>\nAnswer:<br \/>\nP = 8(a + b + c + d + e)<br \/>\n93 ft = 8(18 + 18 + 15 + d + 15)<br \/>\nd = 93\/528<br \/>\nd = 0.17<\/p>\n<p>Question 58.<br \/>\n<strong>SIMPLIFYING AND SOLVING<\/strong> Compare and contrast the two problems.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-14.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 14\" width=\"535\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-14.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-14-300x62.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><br \/>\nAnswer:<br \/>\n2(x + 3) &#8211; 4<br \/>\n= 2x + 6 &#8211; 4<br \/>\n= 2x + 2<\/p>\n<p>Question 59.<br \/>\n<strong>PUZZLE<\/strong><br \/>\nIn a magic square, the sum of the numbers in each row, column, and diagonal is the same. Find the values of a, b, and c. Justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-15.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 15\" width=\"125\" height=\"126\" \/><br \/>\nAnswer:<br \/>\nThe sum of rows and columns is 53.<br \/>\na = 22<br \/>\nb = 0<br \/>\nc = 0<\/p>\n<p>Question 60.<br \/>\n<strong>REASONING<\/strong><br \/>\nOn Saturday, you spend $33, give $15 to a friend, and receive $20 for mowing your neighbor\u2019s lawn. You have $21 left. Use two methods to find how much money you started with that day.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nOn Saturday, you spend $33, give $15 to a friend, and receive $20 for mowing your neighbor\u2019s lawn.<br \/>\nYou have $21 left.<br \/>\nx = a + b + c &#8211; d<br \/>\nx = 33 + 15 + 20 &#8211; 21<br \/>\nx = 68 &#8211; 21<br \/>\nx = 47<\/p>\n<p>Question 61.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have $15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25705\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-16.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations 6.2 16\" width=\"583\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-16.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-6.2-16-300x135.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><br \/>\na. How much money do you have left if you ride each ride once?<br \/>\nb. Do you have enough money to ride each ride twice? Explain.<br \/>\nAnswer:<br \/>\na. bumper cost : $1.75<br \/>\nsuper pendulum : $1.25 + $1.50= $2.75<br \/>\ngiant slide :\u00a0 $1.75-$0.50= $1.25<br \/>\nferris wheels : $1.50+$0.50=$2<br \/>\ntotal money spent=$7.75<br \/>\nmoney left=$7.75-$15=$7.25<\/p>\n<p>b. No,<br \/>\nmoney required to ride once =$7.75<br \/>\ntotal money required to ride twice=$7.75+$7.75=$15.5<\/p>\n<p>Question 62.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nConsider the equation 15 \u2212 y = 8. Explain how you can solve the equation using the Addition and Subtraction Properties of Equality.<br \/>\nAnswer:<br \/>\n15 \u2212 y = 8<br \/>\n15 = 8 + y<br \/>\n8 + y = 15<br \/>\ny = 15 &#8211; 8<br \/>\ny = 7<\/p>\n<h3><a id=\"Lesson_6.3_Solving_Equations_Using_Multiplication_or_Division\"><\/a>Lesson 6.3 Solving Equations Using Multiplication or Division<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Solving an Equation Using a Tape Diagram<br \/>\nWork with a partner. A student solves an equation using the tape diagrams below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 1\" width=\"555\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-1.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-1-300x104.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><br \/>\na. What equation did the student solve? What is the solution?<\/p>\n<p>Answer:<br \/>\nax = b<br \/>\n4x = 20<br \/>\nx = 20\/4<br \/>\nx = 5<\/p>\n<p>b. Explain how the tape diagrams in Steps 2 and 3 relate to the equation and its solution.<br \/>\nAnswer:<br \/>\nStep 2 and step 3 shows that x = 5<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Solving an Equation Using a Model<br \/>\nWork with a partner. Three robots go out to lunch. They decide to split the $12 bill evenly. The scale represents the number of robots and the price of the meal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25707\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 2\" width=\"445\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-2.png 445w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-2-300x174.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><br \/>\na. How much does each robot pay?<\/p>\n<p>Answer:<br \/>\nThree robots go out to lunch.<br \/>\nThey decide to split the $12 bill evenly.<br \/>\n12\/3 = 4<br \/>\nThus each robot pay $4.<\/p>\n<p>b. When you triple the weight on one side of a balanced scale, what can you do to balance the scale? What if you divide the weight on one side of a balanced scale in half? How does this relate to solving an equation?<br \/>\nc. Use a model to solve 5x = 15. Describe how you can solve the equation algebraically.<br \/>\nAnswer:<br \/>\n5x = 15<br \/>\nx = 15\/5<br \/>\nx = 3<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{a}{8}\\) = 6<br \/>\nAnswer: a = 48<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n\\(\\frac{a}{8}\\) = 6<br \/>\na = 6 \u00d7 8<br \/>\na = 48<\/p>\n<p>Question 2.<br \/>\n14 = \\(\\frac{2y}{5}\\)<br \/>\nAnswer: y = 35<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n14 = \\(\\frac{2y}{5}\\)<br \/>\n14 \u00d7 5 = 2y<br \/>\n2y = 70<br \/>\ny = 70\/2<br \/>\ny = 35<\/p>\n<p>Question 3.<br \/>\n3z \u00f7 2 = 9<br \/>\nAnswer: z = 6<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n3z \u00f7 2 = 9<br \/>\n3z = 9 \u00d7 2<br \/>\n3z = 18<br \/>\nz = 18\/3<br \/>\nz = 6<\/p>\n<p>Question 4.<br \/>\np . 3 = 18<br \/>\nAnswer: p = 6<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\np . 3 = 18<br \/>\np = 18\/3<br \/>\np = 6<\/p>\n<p>Question 5.<br \/>\n12q = 60<br \/>\nAnswer: q = 5<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n12q = 60<br \/>\nq = 60\/12<br \/>\nq = 5<\/p>\n<p>Question 6.<br \/>\n81 = 9r<br \/>\nAnswer: r = 9<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n81 = 9r<br \/>\nr = 81\/9<br \/>\nr = 9<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>SOLVING EQUATIONS<\/strong> Solve the equation. Check your solution.<br \/>\nQuestion 7.<br \/>\n6 = \\(\\frac{2y}{3}\\)<br \/>\nAnswer: y = 9<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n6 = \\(\\frac{2y}{3}\\)<br \/>\n6 \u00d7 3 = 2y<br \/>\n2y = 18<br \/>\ny = 18\/2<br \/>\ny = 9<\/p>\n<p>Question 8.<br \/>\n8s = 56<br \/>\nAnswer: s = 7<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n8s = 56<br \/>\ns = 56\/8<br \/>\ns = 7<\/p>\n<p>Question 9.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich equation does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25708\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-3.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 3\" width=\"370\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-3.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-3-300x43.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\nAnswer: \\(\\frac{1}{4}\\)x = 27 does not belong with the other three.<br \/>\nBecause<br \/>\n3x= 36<br \/>\nx = 36\/3<br \/>\nx = 12<br \/>\n3\/4 x = 9<br \/>\n3x = 36<br \/>\nx = 36\/3<br \/>\nx = 12<br \/>\n4x = 48<br \/>\nx = 48\/4<br \/>\nx = 12<\/p>\n<p><strong>STRUCTURE<\/strong> Just by looking at the equation, find the value of x. Explain your reasoning.<br \/>\nQuestion 10.<br \/>\n5x + 3x = 5x + 18<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nx(5+3)=5x+18<br \/>\n8x=5x+18<br \/>\n8x-5x=18<br \/>\n3x=18<br \/>\nx=18\/3<br \/>\nx=6<\/p>\n<p>Question 11.<br \/>\n8x + \\(\\frac{x}{2}\\) = 8x + 6<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n8x + \\(\\frac{x}{2}\\) = 8x + 6<br \/>\nx (8 + \\(\\frac{1}{2}\\) ) = 8x + 6<br \/>\n8.5x = 8x + 6<br \/>\n8.5x &#8211; 8x = 6<br \/>\n0.5x = 6<br \/>\nx = 6\/0.5<br \/>\nx = 12<\/p>\n<p>Question 12.<br \/>\nThe area of the screen of the smart watch is shown. What are possible dimensions for the length and the width of the screen? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-4.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 4\" width=\"112\" height=\"208\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nArea = 1625 sq.mm<br \/>\nL = 65 mm<br \/>\nW = 25 mm<br \/>\nWe know that,<br \/>\nArea of the rectangle = l \u00d7 w<br \/>\n1625 = 65 \u00d7 25<br \/>\nThus the length and width of the smart watch is 65 mm and 25 mm.<\/p>\n<p>Question 13.<br \/>\nA rock climber climbs at a rate of 720 feet per hour. Write and solve an equation to find the number of minutes it takes for the rock climber to climb 288 feet.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA rock climber climbs at a rate of 720 feet per hour.<br \/>\nThe equation is y = 12x<br \/>\nIt takes 24 minutes for the rock climber to get 288 feet<br \/>\n288 = 12x<br \/>\n288\/12 = 12x\/12<br \/>\n24 = x<br \/>\nNow we have time in minutes that it takes to get 288 feet.<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA gift card stores data using a black, magnetic stripe on the back of the card. Find the width w of the stripe.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25710\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-5.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 5\" width=\"176\" height=\"274\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nArea = 46 \\(\\frac{3}{4}\\) sq. cm<br \/>\nL = 8 \\(\\frac{1}{2}\\) cm<br \/>\nw = 4 cm + x+ \\(\\frac{2}{3}\\) cm<br \/>\nWe know that,<br \/>\nArea of the rectangle = l \u00d7 w<br \/>\n46 \\(\\frac{3}{4}\\) = 4 cm + x+ \\(\\frac{2}{3}\\) \u00d7 8 \\(\\frac{1}{2}\\)<br \/>\n= (4 + 0.6 + x) \u00d7 8.5<br \/>\n46.75 = 34 + 5.4 + 8.5x<br \/>\n8.5x = 46.75 &#8211; 34 &#8211; 5.1<br \/>\n8.5x = 7.6<br \/>\nx = 7.6\/8.5<br \/>\nx = 0.89<br \/>\nThus the width is 0.89 cm<\/p>\n<h3><a id=\"Solving_Equations_Using_Multiplication_or_Division_Homework_&amp;_Practice_6.3\"><\/a>Solving Equations Using Multiplication or Division Homework &amp; Practice 6.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><br \/>\n<strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 1.<br \/>\ny &#8211; 5 = 6<br \/>\nAnswer: y = 11<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\ny &#8211; 5 = 6<br \/>\ny = 6 + 5<br \/>\ny = 11<\/p>\n<p>Question 2.<br \/>\nm + 7 = 8<br \/>\nAnswer: 1<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\nm + 7 = 8<br \/>\nm = 8 &#8211; 7<br \/>\nm = 1<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{7}{8}\\) = \\(\\frac{1}{4}\\) + 9<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{4}\\) + 9 = \\(\\frac{9}{4}\\)<br \/>\n\\(\\frac{7}{8}\\) \u2260 \\(\\frac{9}{4}\\)<br \/>\nnot a solution<\/p>\n<p>Question 4.<br \/>\nWhat is the value of a<sup>3<\/sup> when a= 4?<br \/>\nA. 12<br \/>\nB. 43<br \/>\nC. 64<br \/>\nD. 81<br \/>\nAnswer: 64<\/p>\n<p>Explanation:<br \/>\na<sup>3<\/sup> when a= 4<br \/>\n4 \u00d7 4 \u00d7 4 = 64<br \/>\nThus the correct answer is option C.<\/p>\n<p><strong>Multiply. Write the answer in simplest form.<\/strong><br \/>\nQuestion 5.<br \/>\n\\(\\frac{1}{5}\\) . \\(\\frac{2}{9}\\)<br \/>\nAnswer:<br \/>\nFor fraction multiplication, multiply the numerators and then multiply the denominators to get<br \/>\n\\(\\frac{1}{5}\\) . \\(\\frac{2}{9}\\) = \\(\\frac{2}{45}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{5}{12}\\) \u00d7 \\(\\frac{4}{7}\\)<br \/>\nAnswer:<br \/>\nFor fraction multiplication, multiply the numerators and then multiply the denominators to get<br \/>\n\\(\\frac{5}{12}\\) \u00d7 \\(\\frac{4}{7}\\) = \\(\\frac{5}{21}\\)<\/p>\n<p>Question 7.<br \/>\n2\\(\\frac{1}{3}\\) . \\(\\frac{3}{10}\\)<br \/>\nAnswer:<br \/>\nFor fraction multiplication, multiply the numerators and then multiply the denominators to get<br \/>\n2\\(\\frac{1}{3}\\) = \\(\\frac{7}{3}\\)<br \/>\n\\(\\frac{7}{3}\\) \u00d7 \\(\\frac{3}{10}\\) = \\(\\frac{21}{30}\\)<\/p>\n<p>Question 8.<br \/>\n1\\(\\frac{3}{4}\\) \u00d7 2\\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\n1\\(\\frac{3}{4}\\) = \\(\\frac{7}{4}\\)<br \/>\n2\\(\\frac{2}{3}\\) = \\(\\frac{8}{4}\\)<br \/>\n\\(\\frac{7}{4}\\) \u00d7 \\(\\frac{8}{4}\\) = \\(\\frac{56}{16}\\)<\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25711\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-6.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 6\" width=\"49\" height=\"57\" \/><br \/>\nAnswer: 0.36<\/p>\n<p>Explanation:<br \/>\nMultiply the two decimals<br \/>\n0.4 \u00d7 0.9 = 0.36<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25712\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-7.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 7\" width=\"54\" height=\"64\" \/><br \/>\nAnswer: 0.39<\/p>\n<p>Explanation:<br \/>\nMultiply the two decimals<br \/>\n0.78 \u00d7 0.5 = 0.39<\/p>\n<p>Question 11.<br \/>\n2.63 \u00d7 4.31<br \/>\nAnswer: 11.3353<\/p>\n<p>Explanation:<br \/>\nMultiply the two decimals<br \/>\n2.63 \u00d7 4.31 = 11.3353<\/p>\n<p>Question 12.<br \/>\n1.115 \u00d7 3.28<br \/>\nAnswer: 69.2<\/p>\n<p>Explanation:<br \/>\nMultiply the two decimals<br \/>\n1.115 \u00d7 3.28 = 69.2<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>CHOOSE TOOLS<\/strong> Use a model to solve the equation. (See Explorations 1 and 2, p. 259.)<br \/>\nQuestion 13.<br \/>\n8x = 8<br \/>\nAnswer: 1<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n8x = 8<br \/>\nx = 8\/8<br \/>\nx = 1<\/p>\n<p>Question 14.<br \/>\n9 = 3y<br \/>\nAnswer: 3<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n9 = 3y<br \/>\ny = 9\/3<br \/>\ny = 3<\/p>\n<p>Question 15.<br \/>\n2z = 14<br \/>\nAnswer: 7<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n2z = 14<br \/>\nz = 14\/2<br \/>\nz = 7<\/p>\n<p><strong>SOLVING EQUATIONS<\/strong> Solve the equation. Check your solution.<br \/>\nQuestion 16.<br \/>\n\\(\\frac{s}{10}\\) = 7<br \/>\nAnswer: 70<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n\\(\\frac{s}{10}\\) = 7<br \/>\ns = 7 \u00d7 10<br \/>\ns = 70<\/p>\n<p>Question 17.<br \/>\n6 = \\(\\frac{t}{s}\\)<br \/>\nAnswer: 6s = t<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n6 = \\(\\frac{t}{s}\\)<br \/>\nt = 6s<\/p>\n<p>Question 18.<br \/>\n5x \u00f7 6 = 20<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n5x \u00f7 6 = 20<br \/>\n5x = 20 \u00d7 6<br \/>\n5x = 120<br \/>\nx = 120\/5<br \/>\nx = 24<\/p>\n<p>Question 19.<br \/>\n24 = \\(\\frac{3}{4}\\)r<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n24 = \\(\\frac{3}{4}\\)r<br \/>\n24 \u00d7 4 = 3r<br \/>\n96 = 3r<br \/>\nr = 32<\/p>\n<p>Question 20.<br \/>\n3a = 12<br \/>\nAnswer: 4<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n3a = 12<br \/>\na = 12\/3<br \/>\na = 4<\/p>\n<p>Question 21.<br \/>\n5 . z = 35<br \/>\nAnswer: 7<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n5 . z = 35<br \/>\nz = 35\/5<br \/>\nz = 7<\/p>\n<p>Question 22.<br \/>\n40 = 4y<br \/>\nAnswer: 10<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n40 = 4y<br \/>\n40\/4 = y<br \/>\ny = 10<\/p>\n<p>Question 23.<br \/>\n42 = 7k<br \/>\nAnswer: 6<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n42 = 7k<br \/>\n7k = 42<br \/>\nk = 42\/7<\/p>\n<p>Question 24.<br \/>\n7x = 105<br \/>\nAnswer: 15<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n7x = 105<br \/>\nx = 105\/7<br \/>\nx = 15<\/p>\n<p>Question 25.<br \/>\n75 = 6 . w<br \/>\nAnswer: 12.5<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n75 = 6 . w<br \/>\nw = 75\/6<br \/>\nw = 12.5<\/p>\n<p>Question 26.<br \/>\n13 = d \u00f7 6<br \/>\nAnswer: 78<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n13 = d \u00f7 6<br \/>\nd = 13 \u00d7 6<br \/>\nd = 78<\/p>\n<p>Question 27.<br \/>\n9 = v \u00f7 5<br \/>\nAnswer: 45<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n9 = v \u00f7 5<br \/>\nv = 9 \u00d7 5<br \/>\nv = 45<\/p>\n<p>Question 28.<br \/>\n\\(\\frac{5d}{9}\\) = 10<br \/>\nAnswer: 18<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n\\(\\frac{5d}{9}\\) = 10<br \/>\n5d = 10 \u00d7 9<br \/>\n5d = 90<br \/>\nd = 18<\/p>\n<p>Question 29.<br \/>\n\\(\\frac{3}{5}\\) = 4m<br \/>\nAnswer: 0.15<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n\\(\\frac{3}{5}\\) = 4m<br \/>\n3 = 4m \u00d7 5<br \/>\n20m = 3<br \/>\nm = 3\/20<br \/>\nm = 0.15<\/p>\n<p>Question 30.<br \/>\n136 = 17b<br \/>\nAnswer: 19.4<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n136 = 17b<br \/>\nb = 136\/17<br \/>\nb = 19.4<\/p>\n<p>Question 31.<br \/>\n\\(\\frac{2}{3}\\) = \\(\\frac{1}{4}\\)k<br \/>\nAnswer: 2.6<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n\\(\\frac{2}{3}\\) = \\(\\frac{1}{4}\\)k<br \/>\nk = \\(\\frac{8}{3}\\)<br \/>\nk = 2.6<\/p>\n<p>Question 32.<br \/>\n\\(\\frac{2c}{15}\\) = 8.8<br \/>\nAnswer: 66<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n\\(\\frac{2c}{15}\\) = 8.8<br \/>\n2c = 8.8 \u00d7 15<br \/>\n2c = 132<br \/>\nc = 132\/2<br \/>\nc = 66<\/p>\n<p>Question 33.<br \/>\n7b \u00f7 12 = 4.2<br \/>\nAnswer: 7.2<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n7b \u00f7 12 = 4.2<br \/>\n7b = 4.2 \u00d7 12<br \/>\nb = 7.2<\/p>\n<p>Question 34.<br \/>\n12.5 . n = 32<br \/>\nAnswer: 2.56<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n12.5 . n = 32<br \/>\nn = 32\/12.5<br \/>\nn = 2.56<\/p>\n<p>Question 35.<br \/>\n3.4 m = 20.4<br \/>\nAnswer: m = 6<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n3.4 m = 20.4<br \/>\nm = 20.4\/3.4<br \/>\nm = 6<\/p>\n<p>Question 36.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend solves the equation x \u00f7 4 =28. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-8.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 8\" width=\"114\" height=\"109\" \/><br \/>\nAnswer: Your friend is correct<\/p>\n<p>Explanation:<br \/>\nYour friend solves the equation x \u00f7 4 =28.<br \/>\nx \u00f7 4 = 28<br \/>\nx = 28\/4<br \/>\nx = 7<\/p>\n<p>Question 37.<br \/>\n<strong>ANOTHER WAY<\/strong><br \/>\nShow how you can solve the equation 3x = 9 by multiplying each side by the reciprocal of 3.<br \/>\nAnswer:<br \/>\n3x = 9<br \/>\nx = 9 \u00d7 1\/3<br \/>\nx = 3<\/p>\n<p>Question 38.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nForty-five basketball players participate in a three-on-three tournament. Write and solve an equation to find the number of three-person teams in the tournament.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25714\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-9.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 9\" width=\"276\" height=\"210\" \/><br \/>\nAnswer: 15<\/p>\n<p>Explanation:<br \/>\nLet the number of teams be x<br \/>\nx \u00d7 3 = 45<br \/>\nx = 45\/3<br \/>\nx = 15<\/p>\n<p>Question 39.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA theater has 1200 seats. Each row has 20 seats. Write and solve an equation to find the number of rows in the theater.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA theater has 1200 seats. Each row has 20 seats.<br \/>\nLet x be the number of rows.<br \/>\n1200 = 20 \u00d7 x<br \/>\nx = 1200\/20<br \/>\nx = 60<\/p>\n<p><strong>GEOMETRY<\/strong> Solve for x. Check your answer.<br \/>\nQuestion 40.<br \/>\nArea = 45 square units<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-11.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 11\" width=\"166\" height=\"100\" \/><br \/>\nAnswer:<br \/>\nl = x<br \/>\nw = 5<br \/>\nArea = 45 square units<br \/>\nWe know that,<br \/>\nArea of the Rectangle = l \u00d7 w<br \/>\n45 = x \u00d7 5<br \/>\nx = 45\/5<br \/>\nx = 9 units<\/p>\n<p>Question 41.<br \/>\nArea = 176 square units<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-12.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 12\" width=\"161\" height=\"115\" \/><br \/>\nAnswer:<br \/>\na = 16<br \/>\nArea = 176 square units<br \/>\nWe know that,<br \/>\nArea of the square = a \u00d7 a<br \/>\n176 = 16 \u00d7 x<br \/>\nx = 16<\/p>\n<p>Question 42.<br \/>\n<strong>LOGIC<\/strong><br \/>\nOna test, you earn 92% of the possible points by correctly answering 6 five-point questions and 8 two-point questions. How many points p is the test worth?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nOna test, you earn 92% of the possible points by correctly answering 6 five-point questions and 8 two-point questions.<br \/>\n(6 \u00d7 5) + (8 \u00d7 2) = 46<br \/>\n92 \u00d7 1\/100 = 46<br \/>\n0.92x = 46<br \/>\nx = 46\/0.92<br \/>\nx = 50<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou use index cards to play a homemade game. The object is to be the first to get rid of all your cards. How many cards are in your friend\u2019s stack?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-13.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 13\" width=\"192\" height=\"117\" \/><br \/>\nAnswer:<br \/>\nThe number of cards in your friend&#8217;s stack divided by the height of your&#8217;s friends stack equals the number of cards in your stack divided by the height of your stack.<br \/>\nx = the number of cards in your friend&#8217;s stack<br \/>\nx \u00f7 5 = 48 \u00f7 12<br \/>\nx \u00f7 5 = 4<br \/>\nx = 4 \u00d7 5<br \/>\nx = 20<\/p>\n<p>Question 44.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA slush drink machine fills 1440 cups in 24 hours.<br \/>\na. Find the number c of cups each symbol represents.<br \/>\nb. To lower costs, you replace the cups with paper cones that hold 20% less. Find the number n of paper cones that the machine can fill in 24 hours.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-14.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 14\" width=\"272\" height=\"295\" \/><br \/>\nAnswer:<br \/>\nThe number of symbols times the number of cups per symbol equals the total number of cups filled.<br \/>\nC = The number of cups filled<br \/>\n30 \u00d7 c = 1440<br \/>\nc = 1440\/30<br \/>\nc = 48<\/p>\n<p>Question 45.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nThe area of the picture is 100 square inches. The length is 4 times the width. Find the length and width of the picture.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-15.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations 6.3 15\" width=\"320\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-15.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations-6.3-15-300x84.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe area of the picture is 100 square inches.<br \/>\nThe length is 4 times the width.<br \/>\nWe know that,<br \/>\nArea of Rectangle = l \u00d7 w<br \/>\n100 sq. in = 4w \u00d7 w<br \/>\n100 = 4w\u00b2<br \/>\nw = \u221a25 = 5<br \/>\nL = 4w<br \/>\nL = 4 \u00d7 5<br \/>\nL = 20<\/p>\n<h3><a id=\"Lesson_6.4_Writing_Equations_in_Two_Variables\"><\/a>Lesson 6.4 Writing Equations in Two Variables<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing Equations in Two Variables<br \/>\nWork with a partner. section 3.4 Exploration 1, you used a ratio table to create a graph for an airplane traveling 300 miles per hour. Below is one possible ratio table and graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 1\" width=\"511\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-1.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-1-300x185.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><br \/>\na. Describe the relationship between the two quantities. Which quantity depends on the other quantity?<\/p>\n<p>Answer: By seeing the above graph we can say that miles depend on hours (time).<\/p>\n<p>b. Use variables to write an equation that represents the relationship between the time and the distance. What can you do with this equation? Provide an example.<br \/>\nc. Suppose the airplane is 1500 miles away from its destination. Write an equation that represents the relationship between time and distance from the destination. How can you represent this relationship using a graph?<br \/>\nAnswer: The relationship between distance and time is distance is inversely proportional to the time.<br \/>\n5x = 1500<\/p>\n<p>An equation in two variables represents two quantities that change in relationship to one another. A solution of an equation in two variables is an ordered pair that makes the equation true.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-4.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 4\" width=\"190\" height=\"187\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Tell whether the ordered pair is a solution of the equation.<\/strong><br \/>\nQuestion 1.<br \/>\ny = 7x, (2, 21)<br \/>\nAnswer: No<\/p>\n<p>Explanation:<br \/>\nGiven the equation y = 7x<br \/>\ny = 7 \u00d7 2<br \/>\ny = 14<br \/>\n21 \u2260 14<br \/>\nThe ordered pair is not the solution.<\/p>\n<p>Question 2.<br \/>\ny = 5x + 1; (3, 16)<br \/>\nAnswer: Yes<\/p>\n<p>Explanation:<br \/>\nGiven the equation y = 5x + 1<br \/>\ny = 5 \u00d7 3 + 1<br \/>\ny = 15 + 1<br \/>\ny = 16<br \/>\nThe ordered pair is the solution.<\/p>\n<p>Question 3.<br \/>\nThe equation y = 10x + 25 represents the amount y(in dollars) in your savings account after x weeks. Identify the independent and dependent variables. How much is in your savings account after 8 weeks?<br \/>\nAnswer:<br \/>\nBecause the amount y remaining depends on the number x weeks.<br \/>\nY is the dependent variable<br \/>\nX is the independent variable<br \/>\ny = 10x + 25<br \/>\nAfter 8 weeks x = 8<br \/>\ny = 10 (8) + 25<br \/>\ny = 80 + 25<br \/>\ny = 105<\/p>\n<p><strong>Graph the equation.<\/strong><br \/>\nQuestion 4.<br \/>\ny = 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53222\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_2.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_2\" width=\"220\" height=\"199\" \/><br \/>\nWhen x = 0<br \/>\ny = 3(0) = 0<br \/>\nA(x,y) = (0,0)<br \/>\nWhen x = 1<br \/>\ny = 3(1) = 3<br \/>\nB(x,y) = (3, 1)<br \/>\nWhen x = 2<br \/>\ny = 3(2) = 6<br \/>\nC(x,y) = (6, 2)<br \/>\nWhen x = 3<br \/>\ny = 3(3) = 9<br \/>\nD(x,y) = (9, 3)<\/p>\n<p>Question 5.<br \/>\ny = 4x + 1<br \/>\nAnswer:<br \/>\ny = 4x + 1<br \/>\nWhen x = 0<br \/>\ny = 4(0) + 1<br \/>\ny = 1<br \/>\nWhen x = 1<br \/>\ny = 4(1) + 1<br \/>\ny = 5<br \/>\nWhen x = 2<br \/>\ny = 4(2) + 1<br \/>\ny = 9<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53225\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_3.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_3\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 6.<br \/>\ny = \\(\\frac{1}{2}\\)x + 2<br \/>\nAnswer:<br \/>\nGiven,<br \/>\ny = \\(\\frac{1}{2}\\)x + 2<br \/>\nwhen x = 0<br \/>\ny = \\(\\frac{1}{2}\\)0 + 2<br \/>\ny = 2<br \/>\nwhen x = 1<br \/>\ny = \\(\\frac{1}{2}\\)1 + 2<br \/>\ny = 2\\(\\frac{1}{2}\\)<br \/>\ny = 2.5<br \/>\nwhen x = 2<br \/>\ny = \\(\\frac{1}{2}\\)2 + 2<br \/>\ny = 1 + 2<br \/>\ny = 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53226\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_4.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_4\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 7.<br \/>\nIt costs $25 to rent a kayak plus $8 for each hour. Write and graph an equation that represents the total cost (in dollars) of renting the kayak.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nIt costs $25 to rent a kayak plus $8 for each hour.<br \/>\ny = 8x + 25<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 8.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe the difference between independent variables and dependent variables.<br \/>\nAnswer:<br \/>\nThe independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.<\/p>\n<p><strong>IDENTIFYING SOLUTIONS<\/strong> Tell whether the ordered pair is a solution of the equation.<br \/>\nQuestion 9.<br \/>\ny = 3x + 8; (4, 20)<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = 3x + 8<br \/>\nx = 4<br \/>\ny = 20<br \/>\n20 = 3(4) 8<br \/>\n20 = 12 + 8<br \/>\n20 = 20<br \/>\nThe above equation is the solution.<\/p>\n<p>Question 10.<br \/>\ny = 6x &#8211; 14; (7, 29)<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = 6x &#8211; 14<br \/>\n29 = 6(7) &#8211; 14<br \/>\n29 = 42 &#8211; 14<br \/>\n29 \u2260 28<br \/>\nThe above equation is not the solution.<\/p>\n<p>Question 11.<br \/>\n<strong>PRECISION<\/strong><br \/>\nExplain how to graph an equation in two variables.<br \/>\nAnswer:<\/p>\n<ul>\n<li>Find three points whose coordinates are solutions to the equation. Organize them in a table.<\/li>\n<li>Plot the points in a rectangular coordinate system. Check that the points line up. &#8230;<\/li>\n<li>Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.<\/li>\n<\/ul>\n<p>Question 12.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich one does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-5.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 5\" width=\"417\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-5.png 417w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-5-300x30.png 300w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><br \/>\nAnswer: n = 4n &#8211; 6 does not belong to the other three equations because we can take n has common and we can solve the equation.<br \/>\nRemaining there is not possible to solve the equation.<\/p>\n<p>Question 13.<br \/>\nA sky lantern rises at an average speed of 8 feet per second. Write and graph an equation that represents the relationship between the time and the distance risen. How long does it take the lantern to rise 100 feet?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-6.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 6\" width=\"157\" height=\"199\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA sky lantern rises at an average speed of 8 feet per second.<br \/>\nthe lantern to rise 100 feet = ?<br \/>\n8 feets = 1 sec<br \/>\n100 feets = 8 \u00d7 x<br \/>\nx = 100\/8<br \/>\nx = 12.5 sec<\/p>\n<p>Question 14.<br \/>\nYou and a friend start biking in opposite directions from the same point. You travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds. How far apart are you and your friend after 15 minutes?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou and a friend start biking in opposite directions from the same point.<br \/>\nYou travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds.<br \/>\nYour distance Y,<br \/>\nY = 108ft\/8 seconds \u00d7 60 sec\/min \u00d7 15 min \u00d7 1mile\/5280 ft<br \/>\nH is determined similarly<br \/>\nTotal distance apart in miles = Y + H<br \/>\nYou have only 36 minutes while he travels for all 40.<\/p>\n<h3><a id=\"Writing_Equations_in_Two_Variables_Homework_&amp;_Practice_6.4\"><\/a>Writing Equations in Two Variables Homework &amp; Practice 6.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><br \/>\n<strong>Solve the equation.<\/strong><br \/>\nQuestion 1.<br \/>\n4x = 36<br \/>\nAnswer: 9<\/p>\n<p>Explanation:<br \/>\nGiven the equation 4x = 36<br \/>\nx = 36\/4<br \/>\nx = 9<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{x}{8}\\) = 5<br \/>\nAnswer: 40<\/p>\n<p>Explanation:<br \/>\nGiven the equation \\(\\frac{x}{8}\\) = 5<br \/>\nx = 5 \u00d7 8<br \/>\nx = 40<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{4x}{3}\\) = 8<br \/>\nAnswer: 6<\/p>\n<p>Explanation:<br \/>\nGiven the equation \\(\\frac{4x}{3}\\) = 8<br \/>\n4x = 8 \u00d7 3<br \/>\n4x = 24<br \/>\nx = 24\/4<br \/>\nx = 6<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{2}{5}\\)x = 6<br \/>\nAnswer: 15<\/p>\n<p>Explanation:<br \/>\nGiven the equation \\(\\frac{2}{5}\\)x = 6<br \/>\n2x = 5 \u00d7 6<br \/>\n2x = 30<br \/>\nx = 30\/2<br \/>\nx = 15<\/p>\n<p><strong>Divide. Write the answer in simplest form.<\/strong><br \/>\nQuestion 5.<br \/>\n3\\(\\frac{1}{2}\\) \u00f7 \\(\\frac{4}{5}\\)<br \/>\nAnswer: 4 \\(\\frac{3}{8}\\)<\/p>\n<p>Explanation:<br \/>\nConvert any mixed numbers to fractions.<br \/>\nThen your initial equation becomes:<br \/>\n3\\(\\frac{1}{2}\\) = \\(\\frac{7}{2}\\)<br \/>\n\\(\\frac{7}{2}\\) \u00d7 \\(\\frac{5}{4}\\)<br \/>\n= \\(\\frac{35}{8}\\)<br \/>\nNow convert the improper fraction to the mixed fraction.<br \/>\n\\(\\frac{35}{8}\\) = 4 \\(\\frac{3}{8}\\)<\/p>\n<p>Question 6.<br \/>\n7 \u00f7 5\\(\\frac{1}{4}\\)<br \/>\nAnswer: 1 \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nConvert any mixed numbers to fractions.<br \/>\nThen your initial equation becomes:<br \/>\n7 \u00f7 5\\(\\frac{1}{4}\\)<br \/>\n5\\(\\frac{1}{4}\\) = \\(\\frac{21}{4}\\)<br \/>\n\\(\\frac{7}{1}\\) \u00f7 \\(\\frac{21}{4}\\) = 1 \\(\\frac{1}{3}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{3}{11}\\) \u00f7 1\\(\\frac{1}{8}\\)<br \/>\nAnswer: \\(\\frac{8}{33}\\)<\/p>\n<p>Explanation:<br \/>\nConvert any mixed numbers to fractions.<br \/>\nThen your initial equation becomes:<br \/>\n\\(\\frac{3}{11}\\) \u00f7 1\\(\\frac{1}{8}\\)<br \/>\n1\\(\\frac{1}{8}\\) = \\(\\frac{9}{8}\\)<br \/>\n\\(\\frac{3}{11}\\) \u00f7 \\(\\frac{9}{8}\\) = \\(\\frac{8}{33}\\)<\/p>\n<p>Question 8.<br \/>\n7\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{1}{3}\\)<br \/>\nAnswer: 5 \\(\\frac{5}{8}\\)<\/p>\n<p>Explanation:<br \/>\nConvert any mixed numbers to fractions.<br \/>\nThen your initial equation becomes:<br \/>\n7\\(\\frac{1}{2}\\) = \\(\\frac{15}{2}\\)<br \/>\n1\\(\\frac{1}{3}\\) = \\(\\frac{4}{3}\\)<br \/>\n\\(\\frac{15}{2}\\) \u00f7 \\(\\frac{4}{3}\\) = \\(\\frac{45}{8}\\)<br \/>\nNow convert the improper fraction to the mixed fraction.<br \/>\n\\(\\frac{45}{8}\\) = 5 \\(\\frac{5}{8}\\)<\/p>\n<p>Question 9.<br \/>\nFind the area of the carpet tile. Then find the area covered by120 carpet tiles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-7.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 7\" width=\"157\" height=\"136\" \/><br \/>\nAnswer:<br \/>\na = 16 in<br \/>\nArea of the square = a \u00d7 a<br \/>\nA = 16 in \u00d7 16 in<br \/>\nA = 256 sq. in<br \/>\nNow we have to find the area covered by120 carpet tiles.<br \/>\n120 \u00d7 256 = 30720<\/p>\n<p><strong>Copy and complete the statement. Round to the nearest hundredth if necessary.<\/strong><br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-8.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 8\" width=\"108\" height=\"34\" \/><br \/>\nAnswer: 800<\/p>\n<p>Explanation:<br \/>\nconvert from meters to centimeters<br \/>\n1 m = 100 cm<br \/>\n8 m = 8 \u00d7 100 cm = 800 cm<br \/>\nThus 8m = 800cm<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-9.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 9\" width=\"108\" height=\"27\" \/><br \/>\nAnswer:<br \/>\nExplanation:<br \/>\nConvert from ounces to pounds<br \/>\n88 oz = 5.5 pounds<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-10.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 10\" width=\"97\" height=\"32\" \/><br \/>\nAnswer: 709 mL<\/p>\n<p>Explanation:<br \/>\nConvert from cups to milliliters<br \/>\n1 cup = 236.588 mL<br \/>\n3 cups = 709 mL<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-11.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 11\" width=\"120\" height=\"34\" \/><br \/>\nAnswer: 9.321 mi<\/p>\n<p>Explanation:<br \/>\nConvert from km to miles<br \/>\n1 km = 0.621 mi<br \/>\n15 km = 15 \u00d7 0.621 mi<br \/>\n15 km = 9.321 miles<\/p>\n<p><strong>Divide.<\/strong><br \/>\nQuestion 14.<br \/>\n\\(\\sqrt [ 6 ]{ 34.8 } \\)<br \/>\nAnswer: 6th root of 34.8 is 1.806<\/p>\n<p>Question 15.<br \/>\n\\(\\sqrt [ 4 ]{ 12.8 } \\)<br \/>\nAnswer: 4th root of 12.8 is 1.891<\/p>\n<p>Question 16.<br \/>\n45.92 \u00f7 2.8<br \/>\nAnswer: 16.2<\/p>\n<p>Explanation:<br \/>\nMultiplying two decimal numbers<br \/>\n45.92 \u00f7 2.8 = 16.2<\/p>\n<p>Question 17.<br \/>\n39.525 \u00f7 4.25<br \/>\nAnswer: 9.3<\/p>\n<p>Explanation:<br \/>\nMultiplying two decimal numbers<br \/>\n39.525 \u00f7 4.25 = 9.3<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>WRITING EQUATIONS<\/strong> Use variables to write an equation that represents the relationship between the time and the distance. (See Exploration 1, p. 265.)<br \/>\nQuestion 18.<br \/>\nAn eagle flies 40 miles per hour.<br \/>\nAnswer:<br \/>\ny = distance, x = time, rate = 40 miles per minute<br \/>\ndistance = rate . time<br \/>\ny = 40 . x<\/p>\n<p>Question 19.<br \/>\nA person runs 175 yards per minute.<br \/>\nAnswer:<br \/>\ny = distance, x = time, rate = 175 yards per minute<br \/>\ndistance = rate . time<br \/>\nso y = 175 . x<\/p>\n<p><strong>IDENTIFYING SOLUTIONS<\/strong> Tell whether the ordered pair is a solution of the equation.<br \/>\nQuestion 20.<br \/>\ny = 4x; (0, 4)<br \/>\nAnswer:<br \/>\nx = 0<br \/>\ny = 4<br \/>\n4 = 4(0)<br \/>\n4 \u2260 0<br \/>\nThe ordered pair is not a solution of the equation.<\/p>\n<p>Question 21.<br \/>\ny = 3x; (2, 6)<br \/>\nAnswer:<br \/>\nx = 2<br \/>\ny = 6<br \/>\ny = 3x<br \/>\n6 = 3(2)<br \/>\n6 = 6<br \/>\nThe ordered pair is a solution of the equation.<\/p>\n<p>Question 22.<br \/>\ny = 5x &#8211; 10; (3, 5)<br \/>\nAnswer:<br \/>\nx = 3<br \/>\ny = 5<br \/>\ny = 5x &#8211; 10<br \/>\n5 = 5(3) &#8211; 10<br \/>\n5 = 15 &#8211; 10<br \/>\n5 = 5<br \/>\nThe ordered pair is a solution of the equation.<\/p>\n<p>Question 23.<br \/>\ny = x + 7; (1, 6)<br \/>\nAnswer:<br \/>\nx = 1<br \/>\ny = 6<br \/>\ny = x + 7<br \/>\n6 = 1 + 7<br \/>\n6 \u2260 8<br \/>\nThe ordered pair is not a solution of the equation.<\/p>\n<p>Question 24.<br \/>\ny = x + 4; (2, 4)<br \/>\nAnswer:<br \/>\nx = 2<br \/>\ny = 4<br \/>\n4 = 2 + 4<br \/>\n4 \u2260 6<br \/>\nThe ordered pair is not a solution of the equation.<\/p>\n<p>Question 25.<br \/>\ny = x &#8211; 5; (6, 11)<br \/>\nAnswer:<br \/>\nx = 6<br \/>\ny = 11<br \/>\n11 = 6 &#8211; 5<br \/>\n11 \u2260 1<br \/>\nThe ordered pair is not a solution of the equation.<\/p>\n<p>Question 26.<br \/>\ny = 6x + 1; (2, 13)<br \/>\nAnswer:<br \/>\nx = 2<br \/>\ny = 13<br \/>\n13 = 6(2) + 1<br \/>\n13 = 12 + 1<br \/>\n13 = 13<br \/>\nThe ordered pair is a solution of the equation.<\/p>\n<p>Question 27.<br \/>\ny = 7x + 2; (2, 0)<br \/>\nAnswer:<br \/>\nx = 2<br \/>\ny = 0<br \/>\n0 = 7(2) + 2<br \/>\n0 = 14 + 2<br \/>\n0 \u2260 16<br \/>\nThe ordered pair is not a solution of the equation.<\/p>\n<p>Question 28.<br \/>\ny = 2x &#8211; 3; (4, 5)<br \/>\nAnswer:<br \/>\nx = 4<br \/>\ny = 5<br \/>\ny = 2x &#8211; 3<br \/>\n5 = 2(4) &#8211; 3<br \/>\n5 = 8 &#8211; 3<br \/>\n5 = 5<br \/>\nThe ordered pair is a solution of the equation.<\/p>\n<p>Question 29.<br \/>\ny = 3x &#8211; 3; (1, 0)<br \/>\nAnswer:<br \/>\nx = 1<br \/>\ny = 0<br \/>\ny = 3x &#8211; 3<br \/>\n0 = 3(1) &#8211; 3<br \/>\n0 = 3 &#8211; 3<br \/>\n0 = 0<br \/>\nThe ordered pair is a solution of the equation.<\/p>\n<p>Question 30.<br \/>\n7 = y &#8211; 5x; (4, 28)<br \/>\nAnswer:<br \/>\nx = 4<br \/>\ny = 28<br \/>\n7 = y &#8211; 5x<br \/>\n7 = 28 &#8211; 5(4)<br \/>\n7 = 28 &#8211; 20<br \/>\n7 \u2260 8<br \/>\nThe ordered pair is not a solution of the equation.<\/p>\n<p>Question 31.<br \/>\ny + 3 = 6x; (3, 15)<br \/>\nAnswer:<br \/>\nx = 3<br \/>\ny = 15<br \/>\ny + 3 = 6x<br \/>\n15 + 3 = 6(3)<br \/>\n18 = 18<br \/>\nThe ordered pair is a solution of the equation.<\/p>\n<p>Question 32.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend determines whether (5, 1) is a solution of y = 3x + 2. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-12.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 12\" width=\"228\" height=\"135\" \/><br \/>\nAnswer:<br \/>\nx = 5<br \/>\ny = 1<br \/>\ny = 3x + 2<br \/>\n1 = 3(5) + 2<br \/>\n1 = 15 + 2<br \/>\n1 \u2260 17<br \/>\nYour friend is correct.<\/p>\n<p><strong>IDENTIFYING VARIABLES<\/strong> Identify the independent and dependent variables.<br \/>\nQuestion 33.<br \/>\nThe equation A = 25w represents the area A (in square feet) of a rectangular dance floor with a width of w feet.<br \/>\nAnswer:<br \/>\nThe area of the dance floor (A) depends on the dance floor<br \/>\nA is the dependent variable<br \/>\nand w is the independent variable<\/p>\n<p>Question 34.<br \/>\nThe equation c= 0.09s represents the amount c(in dollars) of commission a salesperson receives for making a sale of s dollars.<br \/>\nAnswer:<br \/>\nThe commissioner a salesperson receives (c) depends on the sales the salesperson makes<br \/>\nc is dependent variable<br \/>\ns is independent variable<\/p>\n<p>Question 35.<br \/>\nThe equation t = 12p+ 12 represents the total cost t (in dollars) of a meal with a tip of p percent (in decimal form).<br \/>\nAnswer:<br \/>\nThe total cost of a meal depends on the tip of percent<br \/>\nthe dependent variable is t<br \/>\nthe independent variable is p<\/p>\n<p>Question 36.<br \/>\nThe equation h = 60 \u2212 4m represents the height h(in inches) of the water in a tank m minutes after it starts to drain.<br \/>\nAnswer:<br \/>\nThe height of the water (h) depends on the minutes the tank has been draining<br \/>\nthe dependent variable is h<br \/>\nthe independent variable is m<\/p>\n<p><strong>OPEN-ENDED<\/strong> Complete the table by describing possible independent or dependent variables.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-24.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 24\" width=\"539\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-24.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-24-300x80.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><br \/>\nAnswer:<br \/>\n37. Independent variable:<br \/>\nThe grade you receive on the test dependent variable<br \/>\n38. Independent variable:<br \/>\nThe time you reach your destination dependent variable.<br \/>\n39. Dependent variable:<br \/>\nThe amount of minutes used to talk independent variable.<br \/>\n40. Dependent variable:<br \/>\nThe number of hours you work independent variable.<\/p>\n<p><strong>GRAPHING EQUATIONS<\/strong> Graph the equation.<br \/>\nQuestion 41.<br \/>\ny = 2x<br \/>\nAnswer:<br \/>\nGiven,<br \/>\ny = 2x<br \/>\nwhen x = 0<br \/>\ny = 2(0)<br \/>\ny = 0<br \/>\nwhen x = 1<br \/>\ny = 2(1)<br \/>\ny = 2<br \/>\nwhen x = 2<br \/>\ny = 2(2)<br \/>\ny = 4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_5.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_5\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 42.<br \/>\ny = 5x<br \/>\nAnswer:<br \/>\nGiven,<br \/>\ny = 5x<br \/>\nwhen x = 0<br \/>\ny = 5(0)<br \/>\ny = 0<br \/>\nwhen x = 1<br \/>\ny = 5(1)<br \/>\ny = 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_6.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_6\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 43.<br \/>\ny = 6x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_7.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_7\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 44.<br \/>\ny = x + 2<br \/>\nAnswer:<br \/>\nGiven<br \/>\ny = x + 2<br \/>\nwhen x = 0<br \/>\ny = 0 + 2<br \/>\ny = 2<br \/>\n(x, y) = (0,2)<br \/>\nwhen x = 1<br \/>\ny = 1 + 2<br \/>\ny = 3<br \/>\n(x, y) = (1,3)<br \/>\nwhen x = 2<br \/>\ny = 2 + 2<br \/>\ny = 4<br \/>\n(x, y) = (2,4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_8.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_8\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 45.<br \/>\ny = x + 0.5<br \/>\nAnswer:<br \/>\nGiven,<br \/>\ny = x + 0.5<br \/>\nwhen x = 0<br \/>\ny = 0 + 0.5<br \/>\ny = 0.5<br \/>\nwhen x = 1<br \/>\ny = 1 + 0.5<br \/>\ny = 1.5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_9.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_9\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 46.<br \/>\ny = x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_10.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_10\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 47.<br \/>\ny = x + 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_11.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_11\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 48.<br \/>\ny = 3x + 2<br \/>\nAnswer:<br \/>\nGiven,<br \/>\ny = 3x + 2<br \/>\nwhen x = 0<br \/>\ny = 3(0) + 2<br \/>\ny = 0 + 2<br \/>\ny = 2<br \/>\n(x,y) = (0,2)<br \/>\nwhen x = 1<br \/>\ny = 3(1) + 2<br \/>\ny = 3 + 2<br \/>\ny = 5<br \/>\n(x,y) = (1,5)<br \/>\nwhen x = 2<br \/>\ny = 3(2) + 2<br \/>\ny = 6 + 2<br \/>\ny = 8<br \/>\n(x,y) = (2,8)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_12.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_12\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 49.<br \/>\ny = 2x + 4<br \/>\nAnswer:<br \/>\nGiven,<br \/>\ny = 2x + 4<br \/>\nwhen x = 0<br \/>\ny = 2x + 4<br \/>\ny = 2(0) + 4<br \/>\ny = 0 + 4<br \/>\ny = 4<br \/>\nwhen x = 1<br \/>\ny = 2x + 4<br \/>\ny = 2(1) + 4<br \/>\ny = 2 + 4<br \/>\ny = 6<br \/>\nwhen x = 2<br \/>\ny = 2x + 4<br \/>\ny = 2(2) + 4<br \/>\ny = 4 + 4<br \/>\ny = 8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_13.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_13\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 50.<br \/>\ny = \\(\\frac{2}{3}\\)x + 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53246\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_16.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_16\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 51.<br \/>\ny = \\(\\frac{1}{4}\\)x + 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_15.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_15\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 52.<br \/>\ny = 2.5x + 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_14.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_14\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 53.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA cheese pizza costs $5. Additional toppings cost $1.50 each. Write and graph an equation that represents the total cost (in dollars) of a pizza.<br \/>\nAnswer:<br \/>\nLet x be the total cost of pizza<br \/>\nlet x be the number of toppings<br \/>\nTotal cost equals the cost of cheese pizza plus the cost of additional toppings times the number of toppings<br \/>\nThe equation would be x = 5 + 1.50t<br \/>\nTable &amp; Graph:<br \/>\nNumber of toppings\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Total cost, x = 5 + 1.50 t\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Ordered pairs (t, x)<\/p>\n<p>1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(1, 6.50)<br \/>\n2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(2, 8)<br \/>\n3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(3, 9.50)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_1.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_1\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nIt costs $35 for a membership at a wholesale store. The monthly fee is $15. Write and graph an equation that represents the total cost (in dollars) of a membership.<br \/>\nAnswer:<br \/>\nThe equation is y = 35 + 25x<br \/>\nTable &amp; Graph:<br \/>\nNumber of months(x)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Total cost, y = 35 + 25x\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Ordered pairs (t, x)<\/p>\n<p>1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 60\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(1, 60)<br \/>\n2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 85\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(2, 85)<br \/>\n3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 110\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(3, 110)<\/p>\n<p>Question 55.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe maximum size of a text message is 160 characters. A space counts as one character.<br \/>\na. Write an equation that represents the number of remaining (unused) characters in a text message as you type.<br \/>\nb. Identify the independent and dependent variables.<br \/>\nc. How many characters remain in the message shown?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-14.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 14\" width=\"165\" height=\"273\" \/><br \/>\nAnswer:<br \/>\nx = the number of characters used<br \/>\ny = the number of characters unused<br \/>\nThe equation would be y = 160 &#8211; x<br \/>\nThe number of unused characters (y) depends on the number of used character (x)<br \/>\nThe dependent variable is y<br \/>\nThe Independent variable is x<br \/>\nIncluding space and punctuation, 15 characters were used<br \/>\ny = 160 &#8211; x<br \/>\ny = 160 &#8211; 15<br \/>\ny = 145<\/p>\n<p>Question 56.<br \/>\n<strong>CHOOSE TOOLS<\/strong><br \/>\nA car averages 60 miles per hour on a road trip. Use a graph to represent the relationship between the time and the distance traveled.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53259\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_17.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_17\" width=\"220\" height=\"199\" \/><\/p>\n<p><strong>PRECISION<\/strong> Write and graph an equation that represents the relationship between the time and the distance traveled.<br \/>\nQuestion 57.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-15.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 15\" width=\"226\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Ch-6-Answer-Key-img_16.jpg\" alt=\"Big Ideas Math Grade 6 Ch 6 Answer Key img_16\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 58.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-16.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 16\" width=\"234\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53265\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Ch-6-Answer-Key-img_17.jpg\" alt=\"Big Ideas Math Grade 6 Ch 6 Answer Key img_17\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 59.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-17.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 17\" width=\"150\" height=\"105\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Ch-6-Answer-Key-img_18.jpg\" alt=\"Big Ideas Math Grade 6 Ch 6 Answer Key img_18\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 60.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-18.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 18\" width=\"242\" height=\"126\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Ch-6-Answer-Key-img_19.jpg\" alt=\"Big Ideas Math Grade 6 Ch 6 Answer Key img_19\" width=\"220\" height=\"199\" \/><\/p>\n<p><strong>IDENTIFYING SOLUTIONS<\/strong> Fill in the blank so that the ordered pair is a solution of the equation.<br \/>\nQuestion 61.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-19.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 19\" width=\"143\" height=\"36\" \/><br \/>\nAnswer:<br \/>\ny = 8x + 3<br \/>\nx = 1<br \/>\ny = 8(1) + 3<br \/>\ny = 11<br \/>\nThus the ordered pair (1, 11)<\/p>\n<p>Question 62.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-20.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 20\" width=\"161\" height=\"35\" \/><br \/>\nAnswer:<br \/>\ny = 12x + 2<br \/>\ny = 14<br \/>\n14 = 12x + 2<br \/>\n14 &#8211; 2 = 12x<br \/>\n12 = 12x<br \/>\nx = 1<br \/>\nThus the ordered pair (1, 14)<\/p>\n<p>Question 63.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-21.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 21\" width=\"155\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-21.png 155w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-21-150x39.png 150w\" sizes=\"(max-width: 155px) 100vw, 155px\" \/><br \/>\nAnswer:<br \/>\ny = 9x + 4<br \/>\ny = 22<br \/>\n22 = 9x + 4<br \/>\n22 &#8211; 4 = 9x<br \/>\n9x = 18<br \/>\nx = 2<\/p>\n<p>Question 64.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nCan the dependent variable cause a change in the independent variable? Explain.<br \/>\nAnswer:<br \/>\nJust like an independent variable, a dependent variable is exactly what it sounds like. It is something that depends on other factors.<\/p>\n<p>Question 65.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite an equation that has (3, 4) as a solution.<br \/>\nAnswer:<br \/>\nStandard form linear equation<br \/>\nax + by = c<br \/>\nWhen a, b and c are constants<br \/>\nWe want to make two equations that<br \/>\ni. have that form<br \/>\nii. do not have all the same solutions and<br \/>\niii. (3, 4) is a solution to both<br \/>\na(3) + b(4) = c<br \/>\n3a + 4b = c<\/p>\n<p>Question 66.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou walk 5 city blocks in 12 minutes. How many city blocks can you walk in 2 hours?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou walk 5 city blocks in 12 minutes.<br \/>\n12 min = 5 city<br \/>\n2 hours = 120 minutes<br \/>\n120 minutes = 300 minutes<\/p>\n<p>Question 67.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nHow fast should the ant walk to go around the rectangle in 4 minutes?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-22.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 22\" width=\"204\" height=\"187\" \/><br \/>\nAnswer:<br \/>\nFirst find the perimeter of the rectangle<br \/>\nP = 2L + 2W<br \/>\nP = 2(16) + 2(12)<br \/>\nP = 32 + 24 = 56 in<br \/>\nr = d\/t<br \/>\nr = 56\/4<br \/>\nr = 14 in\/min<\/p>\n<p>Question 68.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nTo estimate how far you are from lightning (in miles), count the number of seconds between a lightning flash and the thunder that follows. Then divide the number of seconds by 5. Use two different methods to find the number of seconds between a lightning flash and the thunder that follows when a storm is 2.4 miles away.<br \/>\nAnswer:<br \/>\nIf you count the number of seconds between the flash of lightning and the sound of thunder, and then divide by 5, you&#8217;ll get the distance in miles to the lightning: 5 seconds = 1 mile, 15 seconds = 3 miles, 0 seconds = very close.<\/p>\n<p>Question 69.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe graph represents the cost c (in dollars) of buying n tickets to a baseball game.<br \/>\na. Should the points be connected with a line to show all the solutions? Explain your reasoning.<br \/>\nb. Write an equation that represents the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-6-Equations-6.4-23.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 6 Equations 6.4 23\" width=\"185\" height=\"165\" \/><br \/>\nAnswer: y = 5x + 0.5<\/p>\n<h3><a id=\"Equations_Connecting_Concepts\"><\/a>Equations Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><br \/>\nQuestion 1.<br \/>\nA tornado forms 12.25 miles from a weather station. It travels away from the station at an average speed of 440 yards per minute. How far from the station is the tornado after 30 minutes?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cc-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cc 1\" width=\"168\" height=\"242\" \/><br \/>\nUnderstand the problem.<br \/>\nYou know the initial distance between the tornado and the station, and the average speed the tornado is traveling away from the station. You are asked to determine how far the tornado is from the station after 30 minutes.<\/p>\n<p>Make a plan.<br \/>\nFirst, convert the average speed to miles per minute. Then write an equation that represents the distance d (in miles) between the tornado and the station after t minutes. Use the equation to find the value of d when t = 30.<\/p>\n<p>Solve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<br \/>\nAnswer:<br \/>\n440 \u00d7 30 = 13200<\/p>\n<p>Question 2.<br \/>\nYou buy 96 cans of soup to donate to a food bank. The store manager discounts the cost of each case for a total discount of $40. Use an equation in two variables to find the discount for each case of soup. What is the total cost when each can of soup originally costs $1.20?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cc-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cc 2\" width=\"155\" height=\"76\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou buy 96 cans of soup to donate to a food bank.<br \/>\nThe store manager discounts the cost of each case for a total discount of $40.<br \/>\n1 case = 12 cans<br \/>\nx = 96 cans<br \/>\n96 = 12 \u00d7 x<br \/>\nx = 96\/12<br \/>\nx = 8<br \/>\n8 cases<br \/>\n8 \u00d7 $40 = $320<br \/>\n8 \u00d7 $1.20 = $9.6<\/p>\n<p>Question 3.<br \/>\nThe diagram shows the initial amount raised by an organization for cancer research. A business agrees to donate $2 for every $5 donated by the community during an additional fundraising event. Write an equation that represents the total amount raised (in dollars). How much money does the community need to donate for the organization to reach its fundraising goal?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cc-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cc 3\" width=\"146\" height=\"225\" \/><\/p>\n<p>Answer: 13,000 &#8211; 8000 = 5,000<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Planning the Climb<br \/>\nAt the beginning of this chapter, you watched a STEAM video called \u201cRock Climbing.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cc-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cc 4\" width=\"341\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cc-4.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cc-4-300x156.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<h3><a id=\"Equations_Chapter_Review\"><\/a>Equations Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the definition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cr-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cr 1\" width=\"553\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cr-1.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cr-1-300x44.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use an Example and Non-Example Chart to list examples and non-examples of a concept. Here is an Example and Non-Example Chart for the vocabulary term equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cr-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cr 2\" width=\"278\" height=\"284\" \/><\/p>\n<p>Choose and complete a graphic organizer to help you study the concept.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cr-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations cr 3\" width=\"291\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cr-3.png 291w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-cr-3-150x150.png 150w\" sizes=\"(max-width: 291px) 100vw, 291px\" \/><br \/>\n1. inverse operations<br \/>\n2. solving equations using addition or subtraction<br \/>\n3. solving equations using multiplication or division<br \/>\n4. equations in two variables<br \/>\n5. independent variables<br \/>\n6. dependent variables<\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 1\" width=\"579\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-1-300x36.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p><strong>6.1 Writing Equations in One Variable (pp. 245\u2013250)<\/strong><br \/>\nLearning Target: Write equations in one variable and write equations that represent real-life problems.<\/p>\n<p><strong>Write the word sentence as an equation.<\/strong><br \/>\nQuestion 1.<br \/>\nThe product of a number m and 2 is 8.<br \/>\nAnswer: m \u00d7 2 = 8<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation.<br \/>\nThe phrase product indicates &#8216;\u00d7&#8217;<br \/>\nThe equation would be m \u00d7 2 = 8<\/p>\n<p>Question 2.<br \/>\n6 less than a number t is 7.<br \/>\nAnswer: 6 &#8211; t = 7<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation.<br \/>\nThe phrase less than indicates &#8216;-&#8216;<br \/>\nThe equation would be 6 &#8211; t = 7<\/p>\n<p>Question 3.<br \/>\nA number m increased by 5 is 7.<br \/>\nAnswer: m + 5 = 7<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation.<br \/>\nThe phrase increased indicates &#8216;+&#8217;<br \/>\nThe equation would be m + 5 = 7<\/p>\n<p>Question 4.<br \/>\n8 is the quotient of a number g and 3.<br \/>\nAnswer: g \u00f7 3 = 8<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence in the equation.<br \/>\nThe phrase quotient indicates &#8216;\u00f7&#8217;<br \/>\nThe equation would be g \u00f7 3 = 8<\/p>\n<p>Question 5.<br \/>\nThe height of the 50-milliliter beaker is one-third the height of the 2000-milliliter beaker. Write an equation you can use to find the height (in centimeters) of the 2000-milliliter beaker.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 5\" width=\"250\" height=\"221\" \/><br \/>\nAnswer: y = 3x<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe height of the 50-milliliter beaker is one-third the height of the 2000-milliliter beaker.<br \/>\nLet the height of 2000 ml beaker = x<br \/>\nGiven,<br \/>\nHeight of 50 ml beaker, y = 1\/3 of x<br \/>\nThe equation to find the height of the 2000 ml beaker will be<br \/>\ny = 3x<br \/>\nwhich means the height of the 2000 ml beaker is three times the height of the 500 ml beaker.<br \/>\nTherefore, the equation is y = 3x.<\/p>\n<p>Question 6.<br \/>\nThere are 16 teams in a basketball tournament. After two rounds, 12 teams are eliminated. Write and solve an equation to find the number of teams remaining after two rounds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-6.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 6\" width=\"262\" height=\"178\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThere are 16 teams in a basketball tournament. After two rounds, 12 teams are eliminated.<br \/>\nx = 16<br \/>\ny = 12<br \/>\nNumber of teams remaining after two rounds = z<br \/>\nz = x &#8211; y<br \/>\nz = 16 &#8211; 12<br \/>\nz = 4<\/p>\n<p>Question 7.<br \/>\nWrite an equation that has a solution of x = 8.<br \/>\nAnswer: 4x = 32<\/p>\n<p>Question 8.<br \/>\nWrite a word sentence for the equation y + 3 = 5.<br \/>\nAnswer: The sum of the numbers y and 3 is 5.<\/p>\n<p><strong>6.2 Solving Equations Using Addition or Subtraction (pp. 251\u2013258)<\/strong><br \/>\nLearning Target: Write and solve equations using addition or subtraction.<\/p>\n<p>Question 9.<br \/>\nTell whether x = 7 is a solution of x + 9 = 16.<br \/>\nAnswer: Yes<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\nx + 9 = 16<br \/>\nx = 16 &#8211; 9<br \/>\nx = 7<\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 10.<br \/>\nx &#8211; 1 = 8<br \/>\nAnswer: 9<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\nx &#8211; 1 = 8<br \/>\nx = 8 + 1<br \/>\nx = 9<\/p>\n<p>Question 11.<br \/>\nm + 7 = 11<br \/>\nAnswer: 4<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\nm + 7 = 11<br \/>\nm = 11 &#8211; 7<br \/>\nm = 4<\/p>\n<p>Question 12.<br \/>\n21 = p &#8211; 12<br \/>\nAnswer: 33<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n21 = p &#8211; 12<br \/>\np &#8211; 12 = 21<br \/>\np = 21 + 12<br \/>\np = 33<\/p>\n<p><strong>Write the word sentence as an equation. Then solve the equation.<\/strong><br \/>\nQuestion 13.<br \/>\n5 more than a number x is 9.<br \/>\nAnswer: 5 + x = 9<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence as an equation<br \/>\nThe phrase more than indicates &#8216;+&#8217;<br \/>\nThus the equation would be 5 + x = 9<\/p>\n<p>Question 14.<br \/>\n82 is the difference of a number b and 24.<br \/>\nAnswer: b &#8211; 24 = 82<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence as an equation<br \/>\nThe phrase difference indicates &#8216;-&#8216;<br \/>\nThus the equation would be b &#8211; 24 = 82<\/p>\n<p>Question 15.<br \/>\nA stuntman is running on the roof of a train. His combined speed is the sum of the speed of the train and his running speed. The combined speed is 73 miles per hour, and his running speed is 15 miles per hour. Find the speed of the train.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA stuntman is running on the roof of a train. His combined speed is the sum of the speed of the train and his running speed.<br \/>\nThe combined speed is 73 miles per hour, and his running speed is 15 miles per hour.<br \/>\nSpeed of the train = ?<br \/>\nZ =\u00a0 x &#8211; y<br \/>\nz = 73 &#8211; 15<br \/>\nz = 58<\/p>\n<p>Question 16.<br \/>\nBefore swallowing a large rodent, a python weighs 152 pounds. After swallowing the rodent, the python weighs 164 pounds. Find the weight of the rodent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-16.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 16\" width=\"214\" height=\"143\" \/><br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nBefore swallowing a large rodent, a python weighs 152 pounds.<br \/>\nAfter swallowing the rodent, the python weighs 164 pounds.<br \/>\n164 &#8211; 152 = 12 pounds<\/p>\n<p><strong>6.3 Solving Equations Using Multiplication or Division (pp. 259\u2013264)<\/strong><br \/>\nLearning Target: Write and solve equations using multiplication or division.<\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 17.<br \/>\n6 . q = 54<br \/>\nAnswer: 9<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n6 . q = 54<br \/>\nq = 54\/6<br \/>\nq = 9<\/p>\n<p>Question 18.<br \/>\nk \u00f7 3 = 21<br \/>\nAnswer: 63<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\nk \u00f7 3 = 21<br \/>\nk = 21 \u00d7 3<br \/>\nk = 63<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{5}{7}\\)a = 25<br \/>\nAnswer: 35<\/p>\n<p>Explanation:<br \/>\nGiven the equation<br \/>\n\\(\\frac{5}{7}\\)a = 25<br \/>\n5a = 7 \u00d7 25<br \/>\na = 7 \u00d7 5<br \/>\na = 35<\/p>\n<p>Question 20.<br \/>\nThe weight of an object on the Moon is about 16.5% of its weight on Earth. The weight of an astronaut on the Moon is 24.75 pounds. How much does the astronaut weigh on Earth?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-20.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 20\" width=\"231\" height=\"151\" \/><br \/>\nAnswer: 150 pounds<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe weight of an object on the Moon is about 16.5% of its weight on Earth.<br \/>\nThe weight of an astronaut on the Moon is 24.75 pounds.<br \/>\nLet the astronaut weight on Earth be represented by x.<br \/>\nBased on the information given in the question, thus can be formed into an equation as:<br \/>\n16.5% of x = 24.75<br \/>\n16.5% \u00d7 x = 24.75<br \/>\n16.5\/100 \u00d7 x = 24.75<br \/>\n0.165x = 24.75<br \/>\nx = 24.75\/0.165<br \/>\nx = 150 pounds<br \/>\nThe astronaut weighs 150 pounds on Earth.<\/p>\n<p>Question 21.<br \/>\nWrite an equation that can be solved using multiplication and has a solution of x = 12.<br \/>\nAnswer: 3x = 36<\/p>\n<p>Question 22.<br \/>\nAt a farmers&#8217; market, you buy 4 pounds of tomatoes and 2 pounds of sweet potatoes. You spend 80% of the money in your wallet. How much money is in your wallet before you pay?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-22.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 22\" width=\"183\" height=\"124\" \/><br \/>\nAnswer: The money in your wallet before you pay is 20 dollars<\/p>\n<p>Explanation:<br \/>\nCost of 1 pound of tomato = 3 dollars<br \/>\nTherefore,<br \/>\nCost of 4 pound of tomato = 4 x 3 = 12 dollars<br \/>\nCost of 4 pound of tomato = 12 dollars<br \/>\nCost of 1 pound of sweet potatoes = 2 dollars<br \/>\nTherefore,<br \/>\nCost of 2 pound of sweet potatoes = 2 x 2 = 4 dollars<br \/>\nCost of 2 pounds of sweet potatoes = 4 dollars<br \/>\nThe combined cost spend at the market is:<br \/>\ncost spend at market = Cost of 4 pound of tomato + Cost of 2 pound of sweet potatoes<br \/>\ncost spend at market = 12 + 4 = 16 dollars<br \/>\nYou spent 80% of the money in your wallet<br \/>\nTherefore, 80% of the money in your wallet is equal to 16 dollars<br \/>\nLet x be the money in your wallet<br \/>\nThen, we get<br \/>\n80 % of x = 16<br \/>\n80\/100 \u00d7 x = 16<br \/>\n0.8 x = 16<br \/>\nx = 16\/0.8<br \/>\nx = 20<br \/>\nThus money in your wallet before you pay is $20.<\/p>\n<p><strong>6.4 Writing Equations in Two Variables (pp. 265-272)<\/strong><br \/>\nLearning Target: Write equations in two variables and analyze the relationship between the two quantities.<\/p>\n<p><strong>Tell whether the ordered pair is a solution of the equation.<\/strong><br \/>\nQuestion 23.<br \/>\ny = 3x + 1; (2, 7)<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nx = 2<br \/>\ny = 7<br \/>\n7 = 3(2) + 1<br \/>\n7 = 6 + 1<br \/>\n7 = 7<br \/>\nYes, it is the solution of the equation.<\/p>\n<p>Question 24.<br \/>\ny = 7x &#8211; 4; (4, 22)<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nx = 4<br \/>\ny = 22<br \/>\n22 = 7(4) &#8211; 4<br \/>\n22 = 28 &#8211; 4<br \/>\n22 \u2260 24<br \/>\nNo, it is not the solution of the equation.<\/p>\n<p>Question 25.<br \/>\nThe equation E = 360m represents the kinetic energy E (in joules) of a roller-coaster car with a mass of m kilograms. Identify the independent and dependent variables.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-25.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 25\" width=\"216\" height=\"143\" \/><br \/>\nAnswer: E is the dependent variable<br \/>\nm is the independent variable<\/p>\n<p><strong>Graph the equation.<\/strong><br \/>\nQuestion 26.<br \/>\ny = x + 1<br \/>\nAnswer:<br \/>\nGiven,<br \/>\ny = x + 1<br \/>\nwhen x = 0<br \/>\ny = 0 + 1<br \/>\ny = 1<br \/>\n(x, y)\u00a0 = (0, 1)<br \/>\nwhen x = 1<br \/>\ny = 1 + 1<br \/>\ny = 2<br \/>\n(x, y)\u00a0 = (1, 2)<br \/>\nwhen x = 2<br \/>\ny = 2 + 1<br \/>\ny = 3<br \/>\n(x, y)\u00a0 = (2, 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_19.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_19\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 27.<br \/>\ny = 7x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_20.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_20\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 28.<br \/>\ny = 4x + 3<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\ny = \\(\\frac{1}{2}\\)x + 5<br \/>\nAnswer:<br \/>\nGiven,<br \/>\ny = \\(\\frac{1}{2}\\)x + 5<br \/>\nwhen x = 0<br \/>\ny = \\(\\frac{1}{2}\\)0+ 5<br \/>\ny = 5<br \/>\nwhen x = 0<br \/>\ny = \\(\\frac{1}{2}\\)1+ 5<br \/>\ny = 5\\(\\frac{1}{2}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-6-Equations-img_21.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 6 Equations img_21\" width=\"220\" height=\"199\" \/><\/p>\n<p>Question 30.<br \/>\nA taxi ride costs $3 plus $2.50 per mile. Write and graph an equation that represents the total cost (in dollars) of a taxi ride. What is the total cost of a five-mile taxi ride?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-30.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 30\" width=\"206\" height=\"181\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA taxi ride costs $3 plus $2.50 per mile.<br \/>\n5 \u00d7 2.50 = $25.50<\/p>\n<p>Question 31.<br \/>\nWrite and graph an equation that represents the total cost (in dollars) of renting the bounce house. How much does it cost to rent the bounce house for 6 hours?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-6-Equations-crr-31.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 6 Equations crr 31\" width=\"206\" height=\"182\" \/><br \/>\nAnswer:<br \/>\nC= $25 x 6 = $150<br \/>\n25&#215;6=150+100=250<\/p>\n<p>Question 32.<br \/>\nA car averages 50 miles per hour on a trip. Write and graph an equation that represents the relationship between the time and the distance traveled. How long does it take the car to travel 525 miles?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA car averages 50 miles per hour on a trip.<br \/>\n50 miles &#8211; 1 hour<br \/>\n525 miles &#8211; x<br \/>\n50 \u00d7 x = 525<br \/>\nx = 525\/50<br \/>\nx = 10.50 hours<br \/>\nThus it takes 10.5 hours to travel 525 miles.<\/p>\n<h3><a id=\"Equations_Practice_Test\"><\/a>Equations Practice Test<\/h3>\n<p>Question 1.<br \/>\nWrite \u201c7 times a number is 84\u201d as an equation.<br \/>\nAnswer: 7 \u00d7 n = 84<\/p>\n<p>Explanation:<br \/>\nWe have to write the word sentence into the equation<br \/>\nThe phrase times indicates &#8216;\u00d7&#8217;<br \/>\nThus the equation would be 7 \u00d7 n = 84<\/p>\n<p>Solve the equation. Check your solution.<br \/>\nQuestion 2.<br \/>\n15 = 7 + b<br \/>\nAnswer: b = 8<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n15 = 7 + b<br \/>\nb = 15 &#8211; 7<br \/>\nb = 8<\/p>\n<p>Question 3.<br \/>\nv &#8211; 6 = 16<br \/>\nAnswer: v = 22<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nv &#8211; 6 = 16<br \/>\nv = 16 + 6<br \/>\nv = 22<\/p>\n<p>Question 4.<br \/>\n5x = 70<br \/>\nAnswer: x = 14<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n5x = 70<br \/>\nx = 70\/5<br \/>\nx = 14<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{6m}{7}\\) = 30<br \/>\nAnswer:<br \/>\nGiven,<br \/>\n\\(\\frac{6m}{7}\\) = 30<br \/>\n6m = 30 \u00d7 7<br \/>\n6m = 210<br \/>\nm = 210 \u00f7 6<br \/>\nm = 35<\/p>\n<p>Question 6.<br \/>\nTell whether (3, 27) is a solution of y = 9x<br \/>\nAnswer: solution<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\ny = 9x<br \/>\nx = 3<br \/>\ny = 27<br \/>\n27 = 9(3)<br \/>\n27 = 27<br \/>\nThus the ordered pair is a solution.<\/p>\n<p>Question 7.<br \/>\nTell whether (8, 36) is a solution of y = 4x + 2.<br \/>\nAnswer: not a solution<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\ny = 4x + 2.<br \/>\nx = 8<br \/>\ny = 36<br \/>\n36 = 4(8) + 2<br \/>\n36 = 32 + 2<br \/>\n36 \u2260 34<\/p>\n<p>Question 8.<br \/>\nThe drawbridge shown consists of two identical sections that open to allow boats to pass. Write s an equation you can use to find the length (in feet) of each section of the drawbridge.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-pt-8.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations pt 8\" width=\"237\" height=\"151\" \/><br \/>\nAnswer: 2s = 366ft<\/p>\n<p>Question 9.<br \/>\nEach ticket to a school dance is $4. The total amount collected in ticket sales is $332. Find the number of students attending the dance.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nEach ticket to a school dance is $4.<br \/>\nThe total amount collected in ticket sales is $332.<br \/>\nThe equation would be<br \/>\n4s = 332<br \/>\ns = 83<\/p>\n<p>Question 10.<br \/>\nA soccer team sells T-shirts for a fundraiser. The company that makes the T-shirts charges $10 per shirt plus a $20 shipping fee per order.<br \/>\na. Write and graph an equation that represents the total cost (in dollars) of ordering the shirts.<\/p>\n<p>Answer:<br \/>\nFor this case, the first thing we must do is define variables:<br \/>\nc = total cost<br \/>\nx = x number of shirts.<br \/>\nThe equation that adapts to the problem is:<br \/>\nc (x) = 10x + 20<\/p>\n<p>b. Choose an ordered pair that lies on your graph in part(a). Interpret it in the context of the problem.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-pt-10.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations pt 10\" width=\"121\" height=\"279\" \/><br \/>\nAnswer:<br \/>\nLet&#8217;s choose the next ordered pair:<br \/>\n(x, c (x)) = (0, 20)<br \/>\nWe verify that it is in the graph:<br \/>\nc (20) = 10 (0) + 20<br \/>\nc (20) = 20 (yes, it belongs to the graph).<br \/>\nIn the context of the problem, this point means that the cost per shipment is $ 20<\/p>\n<p>Question 11.<br \/>\nYou hand in 2 homework pages to your teacher. Your teacher now has 32 homework pages to grade. Find the number of homework pages that your teacher originally had to grade.<br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nYou hand in 2 homework pages to your teacher.<br \/>\nYour teacher now has 32 homework pages to grade.<br \/>\n32 &#8211; 2 = 30<\/p>\n<p>Question 12.<br \/>\nWrite an equation that represents the total cost (in dollars) of the meal shown with a tip that is a percent of the check total. What is the total cost of the meal when the tip is 15%?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-pt-12.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations pt 12\" width=\"128\" height=\"157\" \/><br \/>\nAnswer: $41.40<\/p>\n<h3><a id=\"Equations_Cumulative_Practice\"><\/a>Equations Cumulative Practice<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 1\" width=\"294\" height=\"367\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-1.png 294w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-1-240x300.png 240w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><br \/>\nQuestion 1.<br \/>\nYou buy roses at a flower shop for $3 each. How many roses can you buy with $27?<br \/>\nA. 9<br \/>\nB. 10<br \/>\nC. 24<br \/>\nD. 81<br \/>\nAnswer: 9<\/p>\n<p>Explanation:<br \/>\ngiven,<br \/>\nYou buy roses at a flower shop for $3 each.<br \/>\n27\/3 = 9<br \/>\nThus you can buy 9 roses with $27.<br \/>\nThus the correct answer is option A.<\/p>\n<p>Question 2.<br \/>\nYou are making identical fruit baskets using 16 apples, 24 pears, and 32 bananas. What is the greatest number of baskets you can make using all of the fruit?<br \/>\nF. 2<br \/>\nG. 4<br \/>\nH. 8<br \/>\nI. 16<br \/>\nAnswer: 8<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYou are making identical fruit baskets using 16 apples, 24 pears, and 32 bananas.<br \/>\n8 baskets<br \/>\nMULTIPLES OF 16, 24, and, 32<br \/>\n16: 1, 2, 4, 8, 16<br \/>\n24: 1, 2, 3, 4, 6, 8, 12, 24<br \/>\n32: 1, 2, 4, 8, 16, 32<\/p>\n<p>Question 3.<br \/>\nWhich equation represents the word sentence?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 3\" width=\"358\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-3.png 358w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-3-300x41.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><br \/>\nA. 18 &#8211; 5 = 9 &#8211; y<br \/>\nB. 18 + 5 = 9 &#8211; y<br \/>\nC. 18 + 5 = y &#8211; 9<br \/>\nD. 18 &#8211; 5 = y &#8211; 9<br \/>\nAnswer: 18 + 5 = 9 &#8211; y<\/p>\n<p>Explanation:<br \/>\nThe suitable equation for the above word sentence is<br \/>\n18 + 5 = 9 &#8211; y<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 4.<br \/>\nThe tape diagram shows the ratio of tickets sold by you and your friend. How many more tickets did you sell than your friend?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-4.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 4\" width=\"379\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-4.png 379w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-4-300x53.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><br \/>\nF. 6<br \/>\nG. 12<br \/>\nH. 18<br \/>\nI. 30<br \/>\nAnswer: 6<\/p>\n<p>Explanation:<br \/>\nEach rectangle = 6<br \/>\n6 \u00d7 5 = 30<br \/>\n6 \u00d7 2 = 12<br \/>\n30 + 12 = 42<br \/>\nThus the correct answer is option A.<\/p>\n<p>Question 5.<br \/>\nWhat is the value of x that makes the equation true?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-5.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 5\" width=\"72\" height=\"63\" \/><br \/>\n59 + x = 112<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n59 + x = 112<br \/>\nx = 112 &#8211; 59<br \/>\nx = 53<br \/>\nThus the value of x that makes the equation true is 53<\/p>\n<p>Question 6.<br \/>\nThe steps your friend took to divide two mixed numbers are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-6.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 6\" width=\"174\" height=\"168\" \/><br \/>\nWhat should your friend change in order to divide the two mixed numbers correctly?<br \/>\nA. Find a common denominator of 5 and 2.<br \/>\nB. Multiply by the reciprocal of \\(\\frac{18}{5}\\).<br \/>\nC. Multiply by the reciprocal of \\(\\frac{3}{2}\\).<br \/>\nD. Rename 3\\(\\frac{3}{5}\\) as 2\\(\\frac{8}{5}\\).<br \/>\nAnswer:\u00a0 Multiply by the reciprocal of \\(\\frac{3}{2}\\).<\/p>\n<p>Question 7.<br \/>\nA company ordering parts receives a charge of $25 for shipping and handling plus cp$20 per part. Which equation represents the cost (in dollars) of ordering parts?<br \/>\nF. c = 25 + 20p<br \/>\nG. c = 20 + 25p<br \/>\nH. p = 25 + 20c<br \/>\nI. p = 20 + 25c<br \/>\nAnswer: c = 25 + 20p<\/p>\n<p>Question 8.<br \/>\nWhich property is illustrated by the statement?<br \/>\n5(a + 6) = 5(a) + 5(6)<br \/>\nA. Associative Property of Multiplication<br \/>\nB. Commutative Property of Multiplication<br \/>\nC. Commutative Property of Addition<br \/>\nD. Distributive Property<br \/>\nAnswer: Distributive Property<\/p>\n<p>Question 9.<br \/>\nWhat is the value of the expression?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-5.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 5\" width=\"72\" height=\"63\" \/><br \/>\n46.8 \u00f7 0.156<br \/>\nAnswer:<br \/>\nDivide the two decimal numbers<br \/>\nwe get the answer<br \/>\n300<\/p>\n<p>Question 10.<br \/>\nIn the mural below, the squares that are painted red are marked with the letter R.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-10.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 10\" width=\"429\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-10.png 429w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-10-300x157.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><br \/>\nWhat percent of the mural is painted red?<br \/>\nF. 24%<br \/>\nG. 25%<br \/>\nH. 48%<br \/>\nI. 50%<br \/>\nAnswer: 48%<\/p>\n<p>Question 11.<br \/>\nWhich expression is equivalent to 28x + 70?<br \/>\nA. 14 (2x + 5)<br \/>\nB. 14 (5x + 2)<br \/>\nC. 2 (14x + 5)<br \/>\nD. 14 (7x)<br \/>\nAnswer: 14 (2x + 5)<\/p>\n<p>Explanation:<br \/>\n28x + 70<br \/>\nTaking 14 as the common factor<br \/>\n14(2x + 5)<br \/>\nThus the correct answer is option A.<\/p>\n<p>Question 12.<br \/>\nWhat is the first step in evaluating the expression?<br \/>\n3 . (5 + 2)<sup>2<\/sup> \u00f7 7<br \/>\nF. Multiply 3 and 5.<br \/>\nG. Add 5 and 2<br \/>\nH. Evaluate 5<sup>2<\/sup>.<br \/>\nI. Evaluate 2<sup>2<\/sup>.<br \/>\nAnswer: G. Add 5 and 2<\/p>\n<p>Question 13.<br \/>\nJeff wants to save $4000 to buy a used car. He has already saved $850. He plans to save an additional $150 each week.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-6-Equations-cp-13.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 6 Equations cp 13\" width=\"65\" height=\"80\" \/><br \/>\nPart A Write and solve an equation to represent the number of weeks remaining until he can afford the car.<br \/>\nJeff saves $150 per week by saving \\(\\frac{3}{4}\\) of what he earns at his job each week.<br \/>\nHe works 20 hours per week.<br \/>\nPart B Write an equation to represent the amount per hour that Jeff must earn to save $150 per week. Explain your reasoning.<br \/>\nPart C What is the amount per hour that Jeff must earn? Show your work and explain your reasoning.<br \/>\nAnswer: 21 weeks<\/p>\n<p>Explanation:<br \/>\n150 \u00d7 21 = 3150<br \/>\n3150 + 850 = 4000<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>We put all our efforts and experience to prepare Big Ideas Math Book 6th Grade Answer Key Chapter 6 Equations pdf. Hope you are satisfied with the given data and information regarding Big Ideas Math Book 6th Grade Answer Key Chapter 6 Equations. If you have any kind of doubts, clarify with us here. We wish all the very best for all the aspirants preparing for the exam.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Download Big Ideas Math Answers Grade 6 Chapter 6 Equations Pdf for free of cost. If you are browsing for various questions of equations, then here is the one-stop solution. Know the benefit of referring to Big Ideas Math Book 6th Grade Answer Key Chapter 6 Equations. You can learn the tips and simple methods &#8230; <a title=\"Big Ideas Math Answers Grade 6 Chapter 6 Equations\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6-chapter-6\/\" aria-label=\"More on Big Ideas Math Answers Grade 6 Chapter 6 Equations\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":89721,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/04\/Big-Ideas-Math-Answers-Grade-6-Chapter-6-Equations.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/25657"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=25657"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/25657\/revisions"}],"predecessor-version":[{"id":90391,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/25657\/revisions\/90391"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89721"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=25657"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=25657"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=25657"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}