ATwo 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.
BTwo 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.
AYes, see solution.
BNo, see solution.
Practice makes perfect
We want to check whether the number of coupons Querida gave away on Sunday is proportional to the number of hours she worked that day. We know that on Sunday, Querida gave away about 52 coupons an hour. Let's start by finding the number of coupons she gave away in 1, 2, 3, and 4 hours.
Hours Worked on Sunday
1
2
3
4
Coupons Given Away on Sunday
52(1)=52
52(2)=104
52(3)=156
52(4) =208
Let's write the relationships of the number of coupons and hours as ratios in simplest form.
Hours Worked on Sunday
1
2
3
4
Coupons Given Away on Sunday
52
104
156
208
Ratio
52/1=52
104/2=52
156/3=52
208/4=52
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. In this case, each ratio can be simplified to 52, so the number of coupons Querida gave away on Sunday is proportional to the number of hours she worked that day.
We want to check whether the number of coupons Querida gave away on weekend is proportional to the number of hours she worked on Sunday. We know that she gave away 416 coupons on Saturday and 52 coupons an hour on Sunday. Let's start by finding the total number of coupons given away after 1, 2, 3, and 4 hours on Sunday.
Hours Worked on Sunday
1
2
3
4
Coupons Given Away on Weekend
416+ 52(1)=468
416+ 52(2)=520
416+ 52(3)=572
416+ 52(4) =624
Now let's write each relationship of the number of coupons and hours as a ratio in simplest form.
Hours Worked on Sunday
1
2
3
4
Coupons Given Away on Weekend
468
520
572
624
Ratio
468/1=468
520/2=260
572/3
624/4=156
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. In this case, the ratios are not the same, so the number of coupons Querida gave away on the weekend is not proportional to the number of hours she worked on Sunday.
