SOLUTION: 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 rat

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Question 1101871: 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 does each boy have?
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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%28K-38%29%2FS = 2%2F5,           (1)

K%2F%28S-38%29 = 8%2F13.          (2)


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5*(K-38) = 2S,        (3)
13K = 8*(S-38).       (4)


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 5K - 2S =  5*38,     (5)
13K - 8S = -8*38.     (6)



Multiply eq(5) by 4 (both sides). The modified system is

20K - 8S = 20*38,     (7)
13K - 8S = -8*38.     (8)


Now subtract eq(7) from eq(8) (both sides). You will get

20K - 13K = 20*38 - (-8)*38,   or

7K = 20*38 + 8*38 = 28*38  ====>  K = %2828%2A38%29%2F7 = 4*38 = 152.


Then from (5),  2S = 5K - 2*38 = 5*152 - 2*38 = 684  ====>  S = 684%2F2 = 342.


Answer.  K = 152,  S = 342.