1997 Fermat Problem 21

If \dfrac{\left(\frac{a}{c}+\frac{a}{b}+1\right)}{\left(\frac{b}{a}+\frac{b}{c}+1\right)}=11, and a, b, and c are positive integers, then the number of ordered triples (a,b,c), such that a+2b+c\le 40, is

\textbf{(A)}\ 33\quad \textbf{(B)}\ 37\quad \textbf{(C)}\ 40\quad \textbf{(D)}\ 42\quad \textbf{(E)}\ 45

If there are no answer choices shown, enter a numerical answer.

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