IXL | Identify proportional relationships: word problems

Before beginning voice lessons, Tyrone already knew how to sing 4 pieces, and he expects to learn 2 new pieces during each week of lessons. Is the total number of pieces Tyrone knows proportional to the number of weeks he takes lessons?

yes

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Learn with an example

question

Jack earns $12 for each hour of babysitting. Is the amount earned proportional to the number of hours spent babysitting?

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 directly proportional by showing that the relationship can be written as y = kx, where k is a constant ratio.

First, create a chart.

Amount earned (y)	$12	$24	$36	$48
Time spent babysitting (hours) (x)	1	2	3	4

Now divide "Amount earned (y)" by "Time spent babysitting (hours) (x)" to find the ratio (k).

Amount earned (y)	$12	$24	$36	$48
Time spent babysitting (hours) (x)	1	2	3	4
Ratio (k)	12	12	12	12

The ratio is constant (k = 12), so the relationship can be described by the equation y = 12x. This equation means that the amount earned is always 12 times the time spent babysitting (hours).

Because the relationship can be written as y = 12x, the relationship is directly proportional.

Looking for more? Try these:

Lesson: Proportional relationships

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Not feeling ready yet? These can help:

N.7Identify proportional relationships from tables

Identify proportional relationships from equations

Lesson: Proportional relationships

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