The question is as follows:
Each of Paul and Jenny has a whole number of pounds. He says to her: “If you give me £3, I will have $n$ times as much as you”. She says to him: “If you give me £$n$, I will have 3 times as much as you”.
Given that $n$ is a positive integer what are the possible values for $n$?
We begin by representing Paul and Jenny's amounts by $x,y$ respectively.
Then we have:
$x+3 = n(y-3)\\y+n = 3(x-n)$
After some manipulation we can arrive at:
$n = (x+3)/(y-3) = (3x-y)/(4)$
If we let $y-3 = 4$ and $x+3 = 3x-y$ we get a solution but beyond that I'm not quite sure how to progress.
General ideas on how to approach problems like this would be appreciated as well as some help with the solution.