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Expert: - 10/1/2009


Question
A mans age is three times his sons age. Ten years ago he was five times older than his son. By forming two equations and solving them simultaneously, find both of their ages.

???

Thanks, Paul.

Answer
Let M=man and S=son.

The first equation we are given is M = 3S.

Ten years ago refers to M-10 and S-10.  The equation is M-10 = 5(S-10).

Multiply this equation out and put in M = 3S when done.

M - 10 = 5S - 50, so adding 10-5S to both sides gives M - 5S = -40.

Since we have M = 3S, put that in.  Get 3S - 5S = -40, so -2S = -20, so S = 20.
If M is 3S, M is 60.

Check
So the man is 60 and his son is 20, which makes him 3 years older.
Ten years ago, the man was 50 and the son was 10, so he was 5 times older.
It checks, so that's good.

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