Lesson 9
Solving Problems about Proportional Relationships
Problem 1
For each situation, explain whether you think the relationship is proportional or not. Explain your reasoning.
- The weight of a stack of standard 8.5x11 copier paper vs. number of sheets of paper.
- The weight of a stack of different-sized books vs. the number of books in the stack.
![An image of a stack of copier paper.](https://cms-im.s3.amazonaws.com/ogZeR8pYxbW4icyhMS6MWG78?response-content-disposition=inline%3B%20filename%3D%227-7.2.D.PP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.D.PP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T001124Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=28ea7fe599e0280c28858b535a3921fbf1b114fa0dc31a012b422f7ebd76c444)
![An image of 5 different-sized books, stacked on top of one another.](https://cms-im.s3.amazonaws.com/atK4wULuHNdMDJSuca2eDZC8?response-content-disposition=inline%3B%20filename%3D%227-7.2.D.PP.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.D.PP.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T001124Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c2eb7c75ed9b2e9ffdc89cfbcce66ac80c81ebd6f24b573a3a55156beda2e972)
Solution
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Problem 2
Every package of a certain toy also includes 2 batteries.
- Are the number of toys and number of batteries in a proportional relationship? If so, what are the two constants of proportionality? If not, explain your reasoning.
- Use \(t\) for the number of toys and \(b\) for the number of batteries to write two equations relating the two variables.
\(b = \)
\(t = \)
Solution
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Problem 3
Lin and her brother were born on the same date in different years. Lin was 5 years old when her brother was 2.
- Find their ages in different years by filling in the table.
Lin's age Her brother's age 5 2 6 15 25 - Is there a proportional relationship between Lin’s age and her brother’s age? Explain your reasoning.
Solution
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Problem 4
A student argues that \(y=\frac{x}{9}\) does not represent a proportional relationship between \(x\) and \(y\) because we need to multiply one variable by the same constant to get the other one and not divide it by a constant. Do you agree or disagree with this student?
Solution
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(From Unit 2, Lesson 8.)Problem 5
Quadrilateral A has side lengths 3, 4, 5, and 6. Quadrilateral B is a scaled copy of Quadrilateral A with a scale factor of 2. Select all of the following that are side lengths of Quadrilateral B.
5
6
7
8
9
Solution
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(From Unit 1, Lesson 3.)