Diophantus of Alexandria/Arithmetica/Book 1/Problem 15

Problem

 * Two numbers are such that:
 * if the first receives $30$ from the second, they are in the ratio $2 : 1$
 * if the second receives $50$ from the first, they are in the ratio $1 : 3$.

What are these numbers?

Solution

 * The first number is $98$.
 * The second number is $94$.

Proof
Let $x$ and $y$ be the numbers requested.

Then we have: