A6. Two positive numbers $a$ and $b$, with $a>b$, are such that twice their sum is equal to three times their difference. What is the ratio $a: b$ ?
Solution
$5: 1$

The information given can be written as $2(a+b)=3(a-b)$, which upon expansion of the brackets gives $2 a+2 b=3 a-3 b$. After rearrangement we have that $5 b=a$ and so the ratio $a: b$ is $5: 1$.