Question 1101871
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{{{(K-38)/S}}} = {{{2/5}}},           (1)

{{{K/(S-38)}}} = {{{8/13}}}.          (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 = {{{(28*38)/7}}} = 4*38 = 152.


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


<U>Answer</U>.  K = 152,  S = 342.
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