SOLUTION: Five years ago, a man was seven times as old as his niece was at the time. Ten years from now the man will be twice as old as his niece will be. Find the present ages of the man an

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Question 137612: Five years ago, a man was seven times as old as his niece was at the time. Ten years from now the man will be twice as old as his niece will be. Find the present ages of the man and of the girl.
Answer by solver91311(24713) About Me  (Show Source):
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Man's age now: m
Niece's age now: n
Five years ago, the man was m-5, and the niece was n-5, and m-5=7%28n-5%29.

In 10 years, the man will be m%2B10, and the niece will be n%2B10, and m%2B10=2%28n%2B10%29

Rearranging things:
m-5=7%28n-5%29
m-5=7n-35
m-7n=-30

and

m%2B10=2%28n%2B10%29
m%2B10=2n%2B20
m-2n=10

Now all you need to do is solve the system:
m-7n=-30
m-2n=10

And the values of m and n will be the answers you seek.