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

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(52787) (Show Source): You can put this solution on YOUR website!
.

 = ,           (1)

 = .          (2)


================>

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


================>

 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 =  = 4*38 = 152.


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


Answer.  K = 152,  S = 342.

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