Originally Posted by **CaptainBlack**

Not by guessing, exhausive over the ranges involved is not guessing.

And if you don't like exaustive search you can try the following:

$\displaystyle 10x+y=3(x+y) \Rightarrow 7x=2y$,

but $\displaystyle 7$ and $\displaystyle 2$ are prime and so $\displaystyle y$ is a multiple of $\displaystyle 7$,

and as $\displaystyle 7$ is the only single digit non-zero multiple of $\displaystyle 7$

we have $\displaystyle y=7$ and the rest follows.

($\displaystyle y$ has to be non-zero, as if it were zero $\displaystyle x$ would be zero,

which is not permitted).

RonL