Lesson 6: Practice Problems

Problem 1

For each situation, explain whether you think the relationship is proportional or not. Explain your reasoning.

An image of 5 different-sized books, stacked on top of one another.

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.

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.

Lin’s age	Her brother’s age
$5$	$2$
$6$
$15$
	$25$

Problem 4 From Unit 5 Lesson 5

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.