Two quantities are proportional if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional.
Jane's situation, see solution.
Practice makes perfect
Recall that two quantities are proportional if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional. We want to determine which situation represents a proportional relationship between the hours worked and amount earned for Matt and Jane. Let's start by taking a closer look at Matt's earnings.
Matt's Earnings ($ )
12
20
31
Time (h)
1
2
3
We can write the relationships of Matt's earnings and time as ratios in simplest form.
Matt's Earnings ($ )
12
20
31
Time (h)
1
2
3
Ratio ($per h)
12/1=12
20/2=10
31/3
As we can see, the ratios of the two quantities are not the same. This means that the relationship between the hours Matt worked and the amount of money he earns is not proportional. Now let's consider Jane's earnings.
Jane's Earnings ($ )
12
24
36
Time (h)
1
2
3
Like we did before, let's write the relationship between Jane's earnings and the time she works as a ratio in simplest form.
Jane's Earnings ($ )
12
24
36
Time (h)
1
2
3
Ratio ($per h)
12/1=12
24/2=12
36/3=12
We can see that all of the ratios between the two quantities can be simplified to 12. This means that the relationship between the hours Jane worked and amount of money she earned is proportional.
