1992 AHSME Problem 13

How many pairs of positive integers (a,b) with a+b\le 100 satisfy the equation

\frac{a+b^{-1}}{a^{-1}+b}=13?

\text{(A) } 1\quad \text{(B) } 5\quad \text{(C) } 7\quad \text{(D) } 9\quad \text{(E) } 13

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.