Go through the Spectrum Math Grade 6 Answer Key Chapter 3 Lesson 3.5 Problem Solving and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 3 Lesson 3.5 Problem Solving Answers Key
Solve the problems below using ratios and unit rates.
Question 1.
Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 440 miles driven on 20 gallons of gas. How far could you drive on 60 gallons of gas? __________
What is the car’s gas mileage? _______
Answer:
Number of miles driven in a 60 gallons of gas = 132.
The car’s gas mileage is 22miles per 1 gallons of gas.
Explanation:
Number of miles driven in a test of a new car results = 440.
Number of gallons of gas used = 20.
Number of miles driven in a gallons of gas = Number of miles driven in a test of a new car results ÷ Number of gallons of gas used
= \(\frac{440}{20}\)
= 22.
Number of miles driven in a 60 gallons of gas = 60 × Number of miles driven in a gallons of gas
= 60 × 22
= 132.
Question 2.
An ice-cream factory makes 100 quarts of ice cream in 5 hours. How many quarts could be made in 36 hours?
What was that rate per day? _____________
Answer:
Number of quarts made in 36 hours = 720.
Rate per day = 480.
Explanation:
Number of quarts of icecream an ice-cream factory makes = 100.
Number of hours it makes the ice cream = 5.
Number of quarts of icecream an ice-cream factory makes in 1 hour = Number of quarts of icecream an ice-cream factory makes ÷ Number of hours it makes the ice cream
= 100 ÷ 5
= 20.
Number of quarts made in 36 hours = 36 × Number of quarts of icecream an ice-cream factory makes in 1 hour
= 36 × 20
= 720.
Number of quarts made in 24 hours = 24 × Number of quarts of icecream an ice-cream factory makes in 1 hour
= 24 × 20
= 480.
Question 3.
A jet travels 590 miles in 5 hours. At this rate, how far could the jet fly in 10 hours? ______________
What is the rate of speed of the jet? _________
Answer:
Number of miles a jet travels in 10 hour = 1,180.
The rate of speed of the jet is 118 miles per hour.
Explanation:
Number of miles a jet travels = 590.
Number of hours it travels = 5.
Number of miles a jet travels in an hour = Number of miles a jet travels ÷ Number of hours it travels
= 590 ÷ 5
= 118.
Number of miles a jet travels in 10 hour = 10 × Number of miles a jet travels in an hour
= 10 × 118
= 1,180.
Question 4.
You can buy 5 cans of green beans at the Village Market for $2.30, or you can buy 10 of them at
Best Food for $5. 10.
Which place is the better buy? _____________
Answer:
Buying cans at 5 cans of green beans at the Village Market for $2.30 is better than buy 10 of them at
Best Food for $5. 10.
Explanation:
Number of cans of green beans at the Village Market be purchased = 5.
Cost of amount of 5 cans purchased = $2.30.
Cost of 1 can of green beans = Cost of amount of cans purchased ÷ Number of cans of green beans at the Village Market be purchased
= $2.30 ÷ 5
= $0.46.
Cost of 10 apples purchased for $0.46 each = 10 × Cost of 1 can of green beans
= 10 × $0.46
= $4.60.
Number of cans of green beans at the Village Market be purchased = 10.
Cost of amount of 10 cans purchased = $5.10.
Cost of 1 can of green beans = Cost of amount of cans purchased ÷ Number of cans of green beans at the Village Market be purchased
= $5.10 ÷ 10
= $0.51.
Question 5.
You can buy 3 apples at the Quick Stop for $1.29. You can buy 5 apples at Shop and Save for $2.45.
Which place is the better buy? _________
Answer:
Buying 3 apples at the Quick Stop for $1.29 than at a Shop and Save for $2.45.
Explanation:
Number of apples at the Quick Stop can buy = 3.
Cost of 3 apples purchased = $1.29.
Cost of 1 apple = Cost of 3 apples purchased ÷ Number of apples at the Quick Stop can buy
= $1.29 ÷ 3
= $0.43.
Cost of 5 apples for $0.43 = 5 × $0.43
= $2.15.
Number of apples at the Quick Stop can buy = 5.
Cost of 5 apples purchased = $2.45.
Cost of 1 apple = Cost of 5 apples purchased ÷ Number of apples at the Quick Stop can buy
= $2.45 ÷ 5
= $0.49.
Question 6.
A ferris wheel can accommodate 60 people in 15 minutes.
How many people could ride the ferris wheel in 2 hours? ________
What is the rate per hour? _______
Answer:
Number of people a ferris wheel can accommodate in 2 hours = 480.
The rate per hour is 240 people per hour.
Explanation:
Number of people a ferris wheel can accommodate = 60.
Number of minutes it takes = 15.
Number of people a ferris wheel can accommodate in a minute = Number of people a ferris wheel can accommodate ÷ Number of minutes it takes
= 60 ÷ 15
= 4.
Conversion:
1 hour = 60 minutes.
=> 2 hours = 2 × 60
=> 120 minutes.
Number of people a ferris wheel can accommodate in 2 hours = 120 × Number of people a ferris wheel can accommodate in a minute
= 120 × 4
= 480.
Number of people a ferris wheel can accommodate in 1 hour = 60 × Number of people a ferris wheel can accommodate in a minute
= 60 × 4
= 240.
Solve the problems below using ratios and unit rates.
Question 1.
Keith makes 9 out of every 10 free throws. Josie makes 10 out of every 12 free throws. Who is better at making free throws?
_____________ is better at making free throws.
Answer:
Josie is better at making free throws because Josie makes 10 out of 12 and Keith only makes 9.
Explanation:
Number of throws Keith makes = 9.
Total number of Keith throws = 10.
Proportion of Keith makes = Number of throws Keith makes ÷ Total number of Keith throws
= 9 ÷ 10
= 0.9.
Number of throws Josie makes = 10.
Total number of Josie throws = 12.
Proportion of Josie makes = Number of throws Josie makes ÷ Total number of Josie throws
= 10 ÷ 12
= 0.833.
Question 2.
Carl reads 3 books every week. Jonna reads 6 books a month. Ray reads 85 books a year. Who reads the most books?
______________ reads the most books.
Answer:
Carl reads the most books than Jonna and Ray.
Carl reads the most books.
Explanation:
Number of books every week Carl reads = 3.
Conversion:
1 week = 7 days.
Number of books Carl reads a day = Number of books every week Carl reads ÷ 7
= 3 ÷ 7
= 0.428.
Conversion:
1 month = 30 days.
Number of books a month Jonna reads = 6.
Number of books Jonna reads in a day = Number of books a month Jonna reads ÷ 30
= 6 ÷ 30
= 1 ÷ 5
= 0.2.
Conversion:
1 year = 365 days.
Number of books a year Ray reads = 85.
Number of books Ray reads in a day = Number of books a year Ray reads ÷ 365
= 85 ÷ 365
= 0.2328.
Question 3.
Mary runs ‘4laps ¡n 8 minutes. Nicole runs 12 laps in 18 minutes. Who runs faster?
_______________ runs faster.
Answer:
Mary runs faster than Nicole.
Mary runs faster.
Explanation:
Number of laps Mary runs = 4.
Number of minutes Mary runs 4 laps = 8.
Number of laps Mary runs in a minute = Number of laps Mary runs ÷ Number of minutes Mary runs 4 laps
= 4 ÷ 8
= 1 ÷ 2
= 0.5.
Number of laps Nicole runs = 12.
Number of minutes Nicole runs 12 laps = 18.
Number of laps Nicole runs in a minute = Number of laps Nicole runs Number of minutes ÷ Nicole runs 4 laps
= 12 ÷ 18
= 2 ÷ 3
= 0.667.
Question 4.
CD Cuy sells 5 CDs for $‘49. Music Land sells 8 CDs for $59.50. Which store is the better place to buy CDs?
_______ is the better place to buy CDs.
Answer:
Music Land is the better place to buy CD’s than CD Cuy.
Music Land is the better place to buy CDs.
Explanation:
Number of CD’s CD Cuy sells = 5.
Cost of the 5 CD’s CD Cuy sells = $49.
Cost of 1CD CD Cuy sells = Cost of the 5 CD’s CD Cuy sells ÷ Number of CD’s CD Cuy sells
= $49 ÷ 5
= $9.8.
Number of CD’s Music Land sells = 8.
Cost of 8 CD’s Music Land sells = $59.50.
Cost of 1CD’s Music Land sells = Cost of 8 CD’s Music Land sells ÷ Number of CD’s Music Land sells
= $59.50 ÷ 8
= $7.43.
Question 5.
Two classes are ordering pizza for a pizza party. Mrs. Jimenez’s class has 10 students and is planning to share 4 large pizzas. Mr. Nichols’s class has 8 students and will share 3 large pizzas. If everyone in each class will receive the same amount of pizza, will students in Mrs. Jimenez’s class or Mr. Nichols’s class receive more
pizza?
Students in _____________ class will receive more pizza.
Answer:
Mrs. Jimenez’s students will get more pizza than Mr. Nichols students.
Students in Mrs. Jimenez class will receive more pizza.
Explanation:
Number of students Mrs. Jimenez’s class has = 10.
Number of pizzas Mrs. Jimenez is planning to share = 4.
Number of pizzas each student in Mrs. Jimenez gets = Number of pizzas Mrs. Jimenez is planning to share ÷ Number of students Mrs. Jimenez’s class has
= 4 ÷ 10
= 0.4.
Number of students Mr. Nichols’s class has = 8.
Number of pizzas Mr. Nichols is planning to share = 3.
Number of pizzas each student in Mr. Nichols gets = Number of pizzas Mr. Nichols is planning to share ÷ Number of students Mr. Nichols’s class has
= 3 ÷ 8
= 0.375.
Question 6.
Laura earns $7 per hour baby-sitting for her neighbor. How much will Laura make if she baby-sits for 4 hours?
Laura will make ____.
Answer:
Amount of money she earns for 4 hours = $28.
Laura will make $28.
Explanation:
Amount of money Laura earns for baby-sitting for her neighbor = $7.
Number of hours she get $7 = 1.
Amount of money she earns for 4 hours = 4 × Amount of money Laura earns for baby-sitting for her neighbor
= 4 × $7
= $28.