1997 Pascal Problem 22

If \dfrac{97}{19} = w + \dfrac{1}{x + \dfrac{1}{y}}, where w, x, y are all positive integers, then w + x + y equals

\textbf{(A)}\ 16\quad \textbf{(B)}\ 17\quad \textbf{(C)}\ 18\quad \textbf{(D)}\ 19\quad \textbf{(E)}\ 26

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

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.