3.15 If a certain item is sold for $x$ dollars, there is a $15 \%$ loss on the cost, and if it is sold for $y$ dollars, there is a $15 \%$ profit on the cost. Then $y: x$ is
(A) $23: 17$.
(B) $17 y: 23$.
(C) $23 x: 17$.
(D) dependent on the cost.
(E) none of the above.
(20th American High School Mathematics Examination, 1969)
[Solution] Let $c$ be the cost. According to the problem, we have
$$
\left\{\begin{array}{l}
x=c-0.15 c, \\
y=c+0.15 c,
\end{array}\right.
$$
Dividing (2) by (1) gives $\frac{y}{x}=\frac{c+0.15 c}{c-0.15 c}=\frac{1.15}{0.85}=\frac{23}{17}$. Therefore, the answer is $(A)$.