Lesson 6
Solving Problems about Proportional Relationships
Let’s solve 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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143256Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6c7597041389b3694bd2980bdeb62167600b82a29c45674d95e32ca5a91b157c)
![An image of 5 different-sized books, stacked on top of one another.](https://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143256Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=45b4159a18a95fd3674f1f9cd82582747edc1f8369d6b801558c9888338d55cc)
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.
\(b = \)
\(t = \)
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.
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?
Problem 5
In one version of a trail mix, there are 3 cups of peanuts mixed with 2 cups of raisins. In another version of trail mix, there are 4.5 cups of peanuts mixed with 3 cups of raisins. Are the ratios equivalent for the two mixes? Explain your reasoning.