Lesson 9
Solving Rate Problems
Problem 1
This package of sliced cheese costs $2.97.
How much would a package with 18 slices cost at the same price per slice? Explain or show your reasoning.
![An image of a package of cheese slices. At the top of the package “Cheddar Deli Style Cheese” is labeled and at the bottom of the package, in a circle, “11 thin slices” are labeled.](https://staging-cms-im.s3.amazonaws.com/EN4BBsUBEshnEZzQN6DEogbY?response-content-disposition=inline%3B%20filename%3D%226-6.3.B.PP_Image_1.1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.B.PP_Image_1.1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T082532Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1bee640ac27d091e516b996b756199c3b3b0e69c985564cfbad8c36a771e7dd2)
Solution
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Problem 2
A copy machine can print 480 copies every 4 minutes. For each question, explain or show your reasoning.
- How many copies can it print in 10 minutes?
- A teacher printed 720 copies. How long did it take to print?
Solution
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Problem 3
Order these objects from heaviest to lightest.
(Note: 1 pound = 16 ounces, 1 kilogram \(\approx\) 2.2 pounds, and 1 ton = 2,000 pounds)
item | weight |
---|---|
school bus | 9 tons |
horse | 1,100 pounds |
elephant | 5,500 kilograms |
grand piano | 15,840 ounces |
Solution
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Problem 4
Andre sometimes mows lawns on the weekend to make extra money. Two weeks ago, he mowed a neighbor’s lawn for \(\frac{1}{2}\) hour and earned $10. Last week, he mowed his uncle’s lawn for \(\frac{3}{2}\) hours and earned $30. This week, he mowed the lawn of a community center for 2 hours and earned $30.
Which jobs paid better than others? Explain your reasoning.
Solution
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(From Unit 3, Lesson 5.)Problem 5
Calculate and express your answer in decimal form.
- \(\frac12 \boldcdot 17\)
- \(\frac34 \boldcdot 200\)
- \((0.2) \boldcdot 40\)
- \((0.25) \boldcdot 60\)
Solution
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(From Unit 3, Lesson 1.)Problem 6
Here is a polygon.
![A heart-shaped polygon.](https://staging-cms-im.s3.amazonaws.com/ei7i5Ajb6mznQ6FJHydDgxNJ?response-content-disposition=inline%3B%20filename%3D%226-6.1.D.PP.New.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.D.PP.New.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T082532Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9d216fa80d4fc525e4e3f575e2d1649b49fddccbc27cae96e67984fbc46532fe)
- Decompose this polygon so that its area can be calculated. All measurements are in centimeters.
- Calculate its area. Organize your work so that it can be followed by others.
Solution
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(From Unit 1, Lesson 11.)