Engage NY Eureka Math 7th Grade Module 4 Lesson 9 Answer Key
Eureka Math Grade 7 Module 4 Lesson 9 Example Answer Key
Example 1.
The amount of money Tom has is 75% of Sally’s amount of money. After Sally spent $120 and Tom saved all his money, Tom’s amount of money is 50% more than Sally’s. How much money did each have at the beginning? Use a visual model and a percent line to solve the problem.
Answer:
Example 2.
Erin and Sasha went to a candy shop. Sasha bought 50% more candies than Erin. After Erin bought 8 more candies, Sasha had 20% more. How many candies did Erin and Sasha have at first?
a. Model the situation using a visual model.
Answer:
b. How many candies did Erin have at first? Explain.
Answer:
Each bar in the after tape diagram is 8 candies. Sasha has 48 candies. Each bar in the before tape diagram is 16 candies. Erin started with 32 candies.
Example 3.
Kimberly and Mike have an equal amount of money. After Kimberly spent $50 and Mike spent $25, Mike’s money is 50% more than Kimberly’s. How much did Kimberly and Mike have at first?
a. Use an equation to solve the problem.
Answer:
Equation Method:
Let x be the amount of Kimberly’s money, in dollars, after she spent $50. After Mike spent $25, his money is 50% more than Kimberly’s. Mike’s money is also $25 more than Kimberly’s.
0.5x = 25
x = 50
Kimberly started with $100 because 100 – 50 = 50. Mike has $75 because (1.5)50 = 75.
They each started with $100.
b. Use a visual model to solve the problem.
Answer:
Each bar is $25. They both started with $100.
c. Which method do you prefer and why?
Answer:
Answers will vary. I prefer the visual method because it is easier for me to draw the problem out instead of using the algebraic properties.
Eureka Math Grade 7 Module 4 Lesson 9 Exercise Answer Key
Exercise 1.
Todd has 250% more video games than Jaylon. Todd has 56 video games in his collection. He gives Jaylon 8 of his games. How many video games did Todd and Jaylon have in the beginning? How many do they have now?
Answer:
Answers may vary. Sample answer is provided below.
Visual Model:
Each bar in the dark box is 8 games.
Equation Method:
Let z be the number of video games that Jaylon had at the beginning. Then, Todd started with 3.5z video games.
3.5z = 56
z = 16
In the beginning, Jaylon had 16, and Todd had 56. After Todd gave Jaylon 8 of his games, Jaylon had 24, and Todd had 48.
Eureka Math Grade 7 Module 4 Lesson 9 Problem Set Answer Key
Question 1.
Solve each problem using an equation.
a. What is 150% of 625?
Answer:
n = 1.5(625)
n = 937.5
b. 90 is 40% of what number?
Answer:
90 = 0.4(n)
n = 225
c. What percent of 520 is 40? Round to the nearest hundredth of a percent.
Answer:
40 = p(520)
p ≈ 0.0769 = 7.69%
Question 2.
The actual length of a machine is 12.25 cm. The measured length is 12.2 cm. Round the answer to part (b) to the nearest hundredth of a percent.
a. Find the absolute error.
Answer:
|12.2 – 12.25| = 0.05
The absolute error is 0.05 cm.
b. Find the percent error.
Answer:
\(\frac{0.05}{|12.25|}\) × 100% = 0.4082%
percent error ≈ 0.41%
Question 3.
A rowing club has 600 members. 60% of them are women. After 200 new members joined the club, the percentage of women was reduced to 50%. How many of the new members are women?
Answer:
40 of the new members are women.
Question 4.
40% of the marbles in a bag are yellow. The rest are orange and green. The ratio of the number of orange to the number of green is 4:5. If there are 30 green marbles, how many yellow marbles are there? Use a visual model to show your answer.
Answer:
5 units = 30 marbles
1 unit = 30 marbles ÷5 = 6 marbles
4 units = 4 × 6 marbles = 24 marbles
30+24 = 54→60%
18 → 20%
36 → 40%
There are 36 yellow marbles because 40% of the marbles are yellow.
Question 5.
Susan has 50% more books than Michael. Michael has 40 books. If Michael buys 8 more books, will Susan have more or less books than Michael? What percent more or less will Susan’s books be? Use any method to solve the problem.
Answer:
Susan has 25% more.
Question 6.
Harry’s amount of money is 75% of Kayla’s amount of money. After Harry earned $30 and Kayla earned 25% more of her money, Harry’s amount of money is 80% of Kayla’s money. How much money did each have at the beginning? Use a visual model to solve the problem.
Answer:
Each bar is $30. Harry started with $90, and Kayla started with $120.
Eureka Math Grade 7 Module 4 Lesson 9 Exit Ticket Answer Key
Question 1.
Terrence and Lee were selling magazines for a charity. In the first week, Terrance sold 30% more than Lee. In the second week, Terrance sold 8 magazines, but Lee did not sell any. If Terrance sold 50% more than Lee by the end of the second week, how many magazines did Lee sell?
Choose any model to solve the problem. Show your work to justify your answer.
Answer:
Answers may vary.
Equation Model:
Let m be the number of magazines Lee sold.
150% – 130% = 20%, so 0.2m = 8 and m = 40
Visual Model:
20% → 8
100% → 40