Question 57
Let $S$ be the set of ordered pairs $(a, b)$ of positive integers such that $\operatorname{gcd}(a, b)=1$. Compute
$$
\sum_{(a, b) \in S}\left\lfloor\frac{300}{2 a+3 b}\right\rfloor
$$
$$
\sum_{(a, b) \in S}\left\lfloor\frac{300}{2 a+3 b}\right\rfloor
$$