AVERAGE AGE

There are two classes $A$ and $B$. The $average$ age of students of class $A$ is $a$ years and that of class $B$ is $b$ years. The combined average age of students of class $A$ and $B$ is $c$ years. $(a < c < b)$. Let the ratio of number of students in class $A$ to that of class $B$ be $x / y$. ($x$, $y$ are $coprimes$, $x \gt 0, y \gt 0$). Your task is to find $x$ and $y$.