1998 Cayley Problem 23

There are four unequal, positive integers a, b, c, and N such that N = 5a + 3b + 5c. It is also true that N = 4a + 5b + 4c and N is between 131 and 150. What is the value of a + b + c?

\textbf{(A)}\ 13\quad \textbf{(B)}\ 17\quad \textbf{(C)}\ 22\quad \textbf{(D)}\ 33\quad \textbf{(E)}\ 36

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

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