Keith and Shawn each have some money. If Keith spends $38, the ratio of the amount of money Keith has to the amount of money Shawn has will become 2:5. If Shawn spends $38, the ratio will become 8:13. How much money does each boy have?

Answer 1

Keith's amount --- k
Shawn's amount --- s

(k-38)/s = 2/5
5k - 190 = 2s
5k - 2s = 190 (#1)

k/(s-38) = 8/13
13k = 8s - 304
13k - 8s = -304 (#2)

4(#1) - #2 ----> 7k = 1064
k = 152
back in #1
5(152) - 2s = 190
s = 570

Keith had $152 , Shawn had $570