Afather is 32 years older than his son. in four years,
the father will be 5 times as old as his son. how old
is each now?

Step-by-step explanation:

Let s represent the son's age now. Then s+32 is the father's age. In 4 years, we have ...

  5(s+4) = (s+32)+4

  5s +20 = s +36 . . . . . eliminate parentheses

  4s = 16 . . . . . . . . . . . . subtract s+20

  s = 4

The son is now 4 years old; the father, 36.

Alternate solution

In 4 years, the ratio of ages is ...

  father : son = 5 : 1

The difference of their ages at that time is 5-1 = 4 "ratio units". Since the difference in ages is 32 years, each ratio unit must stand for 32/4 = 8 years. That is, the future age ratio is ...

  father : son = 40 : 8

So, now (4 years earlier), the ages must be ...

  father: 36; son: 4.

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