The pair $(x, y)=(2,5)$ is the solution of the system of equations

$$
\begin{aligned}
a x+2 y & =16 \\
3 x-y & =c
\end{aligned}
$$

Determine the value of $\frac{a}{c}$.
Since $(x, y)=(2,5)$ is the solution of the system of equations, then $(x, y)=(2,5)$ satisfies both equations.

Since $(x, y)=(2,5)$ satisfies $a x+2 y=16$, then $2 a+10=16$ or $2 a=6$ and so $a=3$.

Since $(x, y)=(2,5)$ satisfies $3 x-y=c$, then $6-5=c$ or $c=1$.

Therefore, $\frac{a}{c}=3$.

ANSWER: 3