# Struggling with a question at high school level

Jack has 40 dollars more than Jill. Jack gives 20 dollars to Jill. Then they have the same amount of money. I found the answer by method of exhaustion, but how can this be solved more elegantly?

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OOps, forgot the question. Sorry! How much money did Jack and Jill start with? –  ELK Aug 24 '11 at 14:55
If Jack has 40 dollars more than Jill, then trivially they have the same amount of money if Jack gives Jill 20 dollars. So in fact, there are (infinitely) many solutions of the form $(Jack, Jill) = (n + 40, n)$. –  TMM Aug 24 '11 at 14:56

There are multiple solutions to this problem because the second constraint is the same as the first.

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Call Jack's starting amount $k$ (after the last letter of his name), and Jill's $l$. Then we know from the first part of the question that $k-l=40$.
The second part says if $k$ is lowered by 20 and $l$ is raised by 20, they are equal. So $k-20 = l+20$. With basic algebra, this translates to $k-l=40$, so we get the same requirement as the first condition.