Question

Ten years ago a man was three times as old as his son. In twelve more years,the son is three fifths as old as his father.what were their ages 5 years ago?
10 years ago:

son --- x
father --- 3x

NOW:
son --- x+10
father --- 3x+10

12 years from now:
son --- x+22
father -- 3x + 22

x+22 = (3/5)(3x + 22)
times 5
5x + 110 = 9x + 66
-4x = -44
x = 11

so 5 years ago:
son = present age - 5
= (11+10) - 5 = 16
father = 3x+10 - 5 = 38

So 5 years ago, the son was 16, and the father was 38

(right now the son is 21, and the father is 43)

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