Problem

In the expansion of $(p+qx)^4$, the coefficient of $x$ is equal to the coefficient of $x^2$. The constants $p$ and $q$ are both positive.

(a) Find the ratio $p:q$. Give your answer in its simplest form.

(b) It is given that the coefficient of $x^3$ is $486$.

Find the values of $p$ and $q$.