After Jamal spent 3/8 of his money and Caroline spent 3/8 of her money Jamal had $40 more than Caroline

Question

After Jamal spent 3/8 of his money and Caroline spent 3/8 of her money Jamal had $40 more than Caroline. How much money did Caroline have?

Answer 1

let J= amount of money Jamal has

let C= amount of money Caroline has

(5/8)J=amount of money Jamal has left

(5/8)C=amount of money Caroline has left

Jamal had $40 more than Caroline after spending their money

(5/8)J=(5/8)C+40

multiply both sides by (8/5)

(8/5)(5/8)J=(8/5)(5/8)C+(8/5)(40)

J=C+64

Jamal originally had $64 more than Caroline

there are infinitely many answers

Jamal could have had $72 and Caroline $8

(5/8)($72)=$45

(5/8)($8)=$5

$45-$5=$40

Jamal could have had $80 and Caroline $16

(5/8)($80)=$50

(5/8)($16)=$10

$50-$10=$40

to get more whole number answers, use multiples of $8 for Jamal's and Caroline's amounts of money and

make sure the amounts differ by $64