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.