1975 AHSME Problem 17

A man can commute either by train or by bus. If he goes to work on the train in the morning, he comes home on the bus in the afternoon; and if he comes home in the afternoon on the train, he took the bus in the morning. During a total of x working days, the man took the bus to work in the morning 8 times, came home by bus in the afternoon 15 times, and commuted by train (either morning or afternoon) 9 times. Find x.

\begin{array}{l} \textbf{(A)}\ 19 \qquad \textbf{(B)}\ 18 \qquad \textbf{(C)}\ 17 \qquad \textbf{(D)}\ 16 \qquad \\ \textbf{(E)}\ \text{not enough information given to solve the problem} \end{array}

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