If $\frac{97}{19}=w+\frac{1}{x+\frac{1}{y}}$, where $w, x, y$ are all positive integers, then $w+x+y$ equals
(A) 16
(B) 17
(C) 18
(D) 19
(E) 26
Solution

Rewrite $\frac{97}{19}$ as $5+\frac{2}{19}=5+\frac{1}{\left(\frac{19}{2}\right)}$

$$
=5+\frac{1}{9+\frac{1}{2}}
$$

By comparison, $w=5, x=9$ and $y=2$.

Thus, $w+x+y=16$.

ANSWER: (A)

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