SOLUTION: a man is four years older than his wife and 5 times as old as his son.when the son was born the age of the wife is six-seventh of her husband's age.find the age of his wife.

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Question 516355: a man is four years older than his wife and 5 times as old as his son.when the son was born the age of the wife is six-seventh of her husband's age.find the age of his wife.
Answer by Edwin McCravy(20056) About Me  (Show Source):
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>>...a man is four years older than his wife...<< 

M = W + 4

>>...a man is...5 times as old as his son...<<

M = 5S

>>...when the son was born...<<

That was S years ago when

the man's age was M-S and the wife's age was W-S 

the age of the wife was six-seventh of her husband's age.

Therefore W-S = 6%2F7(M-S)

So we have the system of equations:

M = W + 4
M = 5S
W-S = 6%2F7(M-S)

Simplifying the third equation

   7(W - S) = 6(M - S)
    7W - 7S = 6M - 6S
7W - S - 6M = 0

M = W + 4
M = 5S
7W - S - 6M = 0

Solving that system gives 

M = 35, W = 31,  S = 7

Edwin