3. The secretary calculated that she would finish typing the book three hours before the deadline if she typed two pages over the norm each hour, and if she typed four pages over the norm each hour, she would finish five hours before the deadline.

How many pages in total does the secretary need to type, and by what deadline?
Solution.

Let $x$ be the number of pages the secretary is supposed to type each hour, and $y$ be the number of hours required to finish the typing.

The total number of pages the secretary needs to type is $x y$.

(2 points)
\[
\begin{aligned}
\therefore . . .= & \text { The given data in the problem can be expressed by the equation } (x-2)(y-3)=x y \text { and } \\
& \text { the second equation is } (x+4)(y-5)=x y .
\end{aligned}
\]

- (5 points) 2

By rearranging the equations, they become

\[
\begin{array}{r}
-3 x+2 y-6=0 \\
-5 x+4 y-20=0
\end{array}
\]

The solution is $x=8, y=15$.

(5 points)

The secretary needs to type a total of 120 pages, and this should be completed in 15 hours.

(3 points)