## Engage NY Eureka Math 6th Grade Module 1 Lesson 29 Answer Key

### Eureka Math Grade 6 Module 1 Lesson 29 Problem Set Answer Key

Question 1.

Henry has 15 lawns mowed out of a total of 60 lawns. What percent of the lawns does Henry still have to mow?

Answer:

75% of the lawns still need to be mowed.

Question 2.

Marissa got an 85% on her math quiz. She had 34 questions correct. How many questions were on the quiz?

Answer:

There were 40 questions on the quiz.

Question 3.

Lucas read 30% of his book containing 480 pages. What page is he going to read next?

Answer:

30% is 144 pages, so he will read page 145 next.

### Eureka Math Grade 6 Module 1 Lesson 29 Exit Ticket Answer Key

Question 1.

Angelina received two discounts on a $50 pair of shoes. The discounts were taken off one after the other. If she paid $30 for the shoes, what was the percent discount for each coupon? Is there only one answer to this question?

Answer:

Original Price $50

20% off $50 = $10 discount. After a 20% off discount, the new price would be $40.

25% off $40 = $10 discount. After a 25% off discount, the new price would be $30.

Therefore, the two discounts could be 20% off and then 25%.

This is not the only answer. She could have also saved 25% and then 20%.

### Eureka Math Grade 6 Module 1 Lesson 29 Exploratory Challenge Answer Key

Exploratory Challenge 1.

Claim: To find 10% of a number, ail you need to do is move the decimal to the left once.

Use at least one model to solve each problem (e.g., tape diagram, table, double number line diagram, 10 × 10 grid).

a. Make a prediction. Do you think the claim is true or false? ______________ Explain why.

Answer:

Answers will vary. One could think the claim is true because 10% as a fraction is \(\frac{1}{10}\). The same thing happens when one divides by 10 or multiplies by \(\frac{1}{10}\). A student may think the claim is false because it depends on what whole amount represents the number from which the percentage is taken.

b. Determine 10% of 300. _______________

Answer:

300 × \(\frac{1}{10}=\frac{300}{10}\) = 30

c. Find 10% of 80. _____________

Answer:

80 × \(\frac{1}{10}=\frac{80}{10}\) = 8

d. Determine 10% of 64. ________________

Answer:

64 × \(\frac{1}{10}\) = 6.4

e. Find 10% of 5. _______________

Answer:

5 × \(\frac{1}{10}=\frac{5}{10}=\frac{1}{2}\)

f. 10% of_________________ is 48.

Answer:

48 × 10 = 480

g. 10% of _________________ is 6.

Answer:

6 × 10 = 60

h. Gary read 34 pages of a 340-page book. What percent did he read?

Answer:

i. Micah read 16 pages of his book. If this is 10% of the book, how many pages are in the book?

Answer:

There are 160 pages in the book.

j. Using the solutions to the problems above, what conclusions can you make about the claim?

Answer:

The claim is true. When I find 10% of a number, I am really finding \(\frac{1}{10}\) of the amount or dividing by 10, which is the same as what occurred when I moved the decimal point in the number one place to the left.

Exploratory Challenge 2.

Claim: If an item is already on sale, and then there is another discount taken off the new price, this is the same as taking the sum of the two discounts off the original price.

Use at least one model to solve each problem (e.g., tape diagram, table, double number line diagram, 10 × 10 grid).

a. Make a prediction. Do you think the claim is true or false?______________ Explain.

Answer:

The answer is false. They will be different because when two discounts are taken off, the second discount is taken off a new amount.

b. Sam purchased 3 games for $140 after a discount of 30%. What was the original price?

Answer:

c. If Sam had used a 20% off coupon and opened a frequent shopper discount membership to save 10%, would the games still have a total of $140?

Answer:

20% = \(\frac{20}{100}=\frac{2}{10}\) $200 × \(\frac{2}{10}=\frac{\$ 400}{10}\) = $40 saved. The price after the coupon is $160.

10% = \(\frac{10}{100}=\frac{1}{10}\) $160 × \(\frac{1}{10}=\frac{\$ 160}{10}\) = $16 saved. The price after the coupon and discount membership is $144.

No, the games would now total $144.

d. Do you agree with the claim? ______________ Explain why or why not. Create a new example to help support your claim.

Answer:

Do you agree with the claim? NO Explain why or why not. Create a new example to help support your claim.

When two discounts are taken off, the shopper pays more than if both were added together and taken off.

Example:

$100 original price

20%:

100 × \(\frac{2}{10}=\frac{200}{10}\) = 20 saved

$100 – $20 = $80 sale price

Two 10% off discounts:

100 × \(\frac{1}{10}=\frac{100}{10}\) = 10

90 × \(\frac{1}{10}=\frac{90}{10}\) = 9

$100 – $10 – $9 = $81 sale price