IXL | Identify proportional relationships: word problems

Since starting a new recycling plan, Manny's office recycles 3 kilograms of paper each week. Is the total amount of paper recycled proportional to the number of weeks on the new recycling plan?

yes

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Learn with an example

question

Lucy already owns 40 necklaces, and additional necklaces are priced at 1 for a dollar. Is the total number of necklaces Lucy owns proportional to the amount of money Lucy spends on additional necklaces?

yes

key idea

Proportional quantities can be described by the equation y = kx, where k is a constant ratio.

solution

You can check that the relationship is not directly proportional by showing that the relationship cannot be written as y = kx, where k is a constant ratio.

First, create a chart.

Total number of necklaces (y)	41	42	43	44
Money spent on additional necklaces (x)	$1	$2	$3	$4

Now divide "Total number of necklaces (y)" by "Money spent on additional necklaces (x)" to find the ratio (k).

Total number of necklaces (y)	41	42	43	44
Money spent on additional necklaces (x)	$1	$2	$3	$4
Ratio (k)	41	21	14.33...	11

The ratio (k) is not constant, so the relationship can't be described by the equation y = kx, where k is a constant ratio. This means that the relationship is not directly proportional.

Looking for more? Try these:

Lesson: Proportional relationships

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Not feeling ready yet? These can help:

X.7Identify proportional relationships from tables

X.6Identify proportional relationships from graphs and equations

Lesson: Proportional relationships

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