Go through the **Spectrum Math Grade 6 Answer Key Chapter 3 Lesson 3.10 Problem Solving** and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 3 Lesson 3.10 Problem Solving Answers Key

**Solve each problem.**

Question 1.

The sales tax on the purchase of a refrigerator that costs $695 is 7 percent. What is the amount of sales tax?

The sales tax is ____.

Answer:

Amount of sales tax = $486.50.

The sales tax is $486.50.

Explanation:

Cost price of the refrigerator = $695.

Percentage of sales tax = 7%.

Amount of sales tax = Cost price of the refrigerator × Percentage of sales tax

= $695 × 7%

= ($695 × 7) ÷ 100

= $4865 ÷ 100

= $486.50.

Question 2.

A stove that costs $695 will be on sale next week for 28 percent off its regular price. What is the amount of savings?

The savings will be ____.

Answer:

Sales tax amount on the store = $194.60.

Final price of the store = $500.40.

The savings will be $194.60.

Explanation:

Cost price of a stove = $695.

Sales percent of the store next week = 28%.

Sales tax amount on the store = Cost price of a stove × Sales percent of the store next week

= $695 × 28 %

= ($695 × 28) ÷ 100

= $19,460 ÷ 100

= $194.60.

Amount of savings = Regular price of a stove – Sales tax amount on the store

= $695 – $194.60

= $500.40.

Question 3.

In math class, 60 percent of the students are males. There are 30 students in the class. How many students are males?

There are ____ males.

Answer:

Number of students are males = 18.

There are 18 males.

Explanation:

Percentage of students are males in Math class = 60%.

Total students in the class = 30.

Number of students are males = Total students in the class × Percentage of students are males in Math class

= 30 × 60%

= (30 × 60) ÷ 100

= 3 × 6

= 18.

Question 4.

East Side Middle School has 1,500 students. Thirty-two percent of them are in sixth grade. How many sixth-grade students are there?

There are ___________ sixth-grade students.

Answer:

Number of students are sixth-grade = 480.

There are 480 sixth-grade students.

Explanation:

Number of students East Side Middle School has = 1,500.

Percentage of students are in sixth grade = 32%.

Number of students are sixth-grade = Number of students East Side Middle School has × Percentage of students are in sixth grade

= 1,500 × 32%

= (1,500 × 32) ÷ 100

= 15 × 32

= 480.

Question 5.

Lauren is saving for gymnastics camp. Camp costs $225 to attend. She has 40 percent of the money saved. How much money has she saved?

Lauren has saved ______

Answer:

Amount of money she saved = $90.00.

Lauren has saved = $90.00.

Explanation:

Cost to attend Camp = $225.

Percentage of money she saved = 40%.

Amount of money she saved = Cost to attend Camp × Percentage of money she saved

= $225 × 40%

= ($225 × 40) ÷ 100

= $9000 ÷ 100

= $90.00.

Question 6.

Of the 1,500 students attending East Side Middle School, twenty-five percent are running for student council. How many students are running for student council?

____________ students are running for student council.

Answer:

Number of students are running for student council = 375.

375 students are running for student council.

Explanation:

Total number of students attending East Side Middle School = 1,500.

Percentage of students are running for student council = 25%.

Number of students are running for student council = Total number of students attending East Side Middle School × Percentage of students are running for student council

= 1,500 × 25%

= (1500 × 25) ÷ 100

= 15 × 25

= 375.

**Solve each problem.**

Question 1.

The Jacksons’ dinner cost $125. They left $21.25 for a tip. What percent did they tip?

The Jacksons tipped ____.

Answer:

Percentage they tipped = 17%.

The Jacksons tipped 17%.

Explanation:

Cost of the Jacksons’ dinner cost = $125.

Cost of amount they left for a tip = $21.25.

Let the Percentage they tipped be X.

=> Cost of the Jacksons’ dinner cost × Percentage they tipped be = Cost of amount they left for a tip

= $125 × X% = $21.25

= X% = $21.25 ÷ $125

= X% = 0.17

= X ÷ 100 = 0.17

= X = 0.17 × 100

= X = 17.

Question 2.

A sweater was originally $55. It is now marked down to 65% of its original price. How much is the sweater now?

The sweater now costs ____.

Answer:

Cost of the sweater now = $19.25.

The sweater now costs = $19.25.

Explanation:

Cost price of a sweater = $55.

Percentage of a sweater marked down of its original price = 65%.

Cost of marked down on a sweater = Cost price of a sweater × Percentage of a sweater marked down of its original price

= $55 × 65%

= ($55 × 65) ÷ 100

= $3575 ÷ 100

= $35.75.

Cost of the sweater now = Cost price of a sweater ÷ Cost of marked down on a sweater

= $55 – $35.75

= $19.25.

Question 3.

Ms. Martino’s new home cost $260,000. She paid $39,000 in a down payment. What percent of the home cost did she pay in the down payment?

Ms. Martino paid __________ of the total price.

Answer:

Percentage of the home cost she paid in the down payment = 15%.

Ms. Martino paid 15% of the total price.

Explanation:

Cost of the Ms. Martino’s new home = $260,000.

Cost of amount she paid in a down payment = $39,000.

Let the percentage of the home cost she paid in the down payment be X.

=> Cost of the Ms. Martino’s new home × Percentage of the home cost she paid in the down payment = Cost of amount she paid in a down payment

= $260,000 × X% = $39,000

= X% = $39,000 ÷ $260,000

= X% = 0.15.

= X ÷ 100 = 0.15

= X = 0.15 × 100

= X = 15.

Question 4.

Workers have painted 920 square feet of an office. They have completed 80% of their job. How many square feet do they need to paint in all?

They need to paint ____ square feet.

Answer:

Number of square feet they need to paint in all = 184.

They need to paint 184 square feet.

Explanation:

Number of square feet of an office workers have painted = 920.

Percentage of their job they completed = 80%.

Number of square feet they painted = Number of square feet of an office workers have painted × Percentage of their job they completed

= 920 × 80%

= (920 × 80) ÷ 100

= 92 × 8

= 736.

Number of square feet they need to paint in all = Number of square feet of an office workers have painted – Number of square feet they painted

= 920 – 736

= 184.

Question 5.

The Franklins are taking a cross-country trip. They will drive 3,150 miles in all. On the first day, they drove 567 miles. What percent of their trip did they drive?

The Franklins drove ___________ of their trip.

Answer:

Percent of their trip did they drive = 18%.

The Franklins drove 18% of their trip.

Explanation:

Number of miles in all they will drive = 3,150.

Number of miles on first day, they drove = 567.

Let the Percent of their trip did they drive be X.

Number of miles in all they will drive × Percent of their trip did they drive = Number of miles on first day, they drove

= 3150 × X% = 567

= X % = 567 ÷ 3150

= X ÷ 100 = 0.18

= X = 0.18 × 100

= X = 18.

Question 6.

Jen is reading a 276-page book. She is 25% finished. How many pages has she read?

Jen has read __________ pages.

Answer:

Number of pages she read = 69.

Jen has read 69 pages.

Explanation:

Number of page book Jen is reading = 276.

Percentage of she finished = 25%.

Number of pages she read = Number of page book Jen is reading × Percentage of she finished

= 276 × 25%

= (276 × 25) ÷ 100

= 6,900 ÷ 100

= 69.

Question 7.

Pete’s dog weighed 30 pounds. It then lost 16% of its weight. How much did Pete’s dog lose?

The dog lost __________ pounds.

Answer:

Number of pounds Pete’s dog lose = 4.80.

The dog lost 4.80 pounds.

Explanation:

Number of pounds Pete’s dog weighed = 30.

Percentage lost in its weight = 16%.

Number of pounds Pete’s dog lose = Number of pounds Pete’s dog weighed × Percentage lost in its weight

= 30 × 16%

= (30 × 16) ÷ 100

= 480 ÷ 100

= 4.80.

Question 8.

Karla has read 85% of her book, which amounts to 238 pages. How long is the book?

The book is __________ pages long.

Answer:

Total number of pages in the book = 280.

The book is 280 pages long.

Explanation:

Percentage of her book Karla has read = 85%.

Number of pages she read in the book = 238.

Let the total number of pages the book has be X.

=> Total number of pages in the book × Percentage of her book Karla has read = Number of pages she read in the book

= X × 85% = 238

= (X × 85) ÷ 100 = 238

= X × 85 = 238 × 100

= X = 23800 ÷ 85

= X = 280.