Question

10. The ratio of Jill's money and Kelly's money was 4:5. After they each spent $156, the ratio)

became 8:11. How much money did Jill and Kelly have, respectively, at first?

Answer 1

Explanation:

x=Jill's money

y=Kelly's money

x/y=4/5

(x-156)/(y-156)=8/11

x/y=4/5 -------->5x=4y --------->y=5x/4

cross multiply with the above proportion

11(x-156)=8(y-156)

11x-1716=8y-1248

substitute y=5x/4

11x-1716=8(5x/4)-1248

11x-1716=10x-1248

11x-10x=1716-1248

x=$468 for Jill (answer)

x/y=4/5

468/y=4/5

multiply 4 by 117 to get 468

multiply 5 by 117 to get 585

y=$585 for Kelly (answer) (or cross multiply to find y)

Answer 2

Let c be the common factor between Jill and Kelly’s money. Then:

4n-156 / 5n-156=8/11

So:

44n-1716=40n-1248

4n=468

n=117

Jill had 4n, or $468 to begin with

Kelly had 5n, or $585 to begin with ………..