Math CentralQuandaries & Queries


Question from Linda, a parent:

James is now 3/5 John's age. Three years ago, he was 1/2 John's age. Three years from now, he will be 2/3 John's age.
How old are they now?

Hi Linda,

Are you sure you have stated this problem correctly? To solve it I let $m$ be James' age now and $n$ be John's age now. Since "James is now 3/5 John's age." I get

\[m = \frac23 n.\]

Three years ago James' age was $m-3$ and John's age was $n-3.$ Since "Three years ago, he was 1/2 John's age"

\[m-3 = \frac12 (n-3).\]

Solving these equations I got $n=9$ and $m=6.$

The problem I have is that three years from now their ages don't satisfy the condition given in the third sentence of your problem.


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