467. Divide the given number $p$ into two such parts that the sum of the quotients obtained by dividing the first by $m$, and the second by $n$ equals the given number 9.
467. We form the system:

$$
\begin{gathered}
x+y=p \\
\frac{x}{m}+\frac{y}{n}=q
\end{gathered}
$$

from which

$$
x=\frac{m(n q-p)}{n-m} ; y=\frac{n(p-m q)}{n-m}
$$

For example, if

$$
p=17 ; m=3 ; n=4 ; q=5
$$

then

$$
x=9 ; y=8
$$