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I've struggled to solve the following problem analytically:

Ann is $24$ and two times as old as Mary was, when Ann was as old as Mary is now.

The solution to this problem is:

Mary is currently 18 years old.

but I've failed to come up with an analytical way to conclude this. Any ideas?

This is what I've tried:

$$ y_{\text{Ann}} = 24 \;\,\,\text{and}\,\,\; y_{\text{Ann}} = 2 \cdot y_{\text{Mary (at the time Ann was as old Mary is now)}} \\ \Rightarrow \;\;\;\;12 = y_{\text{Mary (at the time Ann was as old Mary is now)}} $$

at this point I got stuck..

user7802048
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1 Answers1

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Let $A,M$ denote their current ages and let $C$ denote the number of years that have elapsed since the prior time under discussion. That is, $C$ is the difference between their two ages.

Then: $$A=24\quad \quad A-C=M\quad \quad A = 2\times (M-C)$$

It is easy to solve this system to get $M=18$.

lulu
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