1. A printing house determines the cost of printing a book as follows: it adds the cost of the cover to the cost of each page, and then rounds the result up to the nearest whole number of rubles (for example, if the result is 202 rubles and 1 kopeck, it is rounded up to 203 rubles). It is known that the cost of a book with 104 pages is 134 rubles, and a book with 192 pages costs 181 rubles. How much does the printing of the cover cost, if it is a whole number of rubles, and the cost of one page is a whole number of kopecks? (20 points)
Solution: Let's convert all costs into kopecks. Let one page cost $x$ kopecks, and the cover cost $100 y$ kopecks. Then, according to the problem, we have

$$
\left\{\begin{array}{l}
13300<100 y+104 x \leq 13400 \\
18000<100 y+192 x \leq 18100
\end{array}\right.
$$

Subtracting the first inequality from the second, we get $4600<88 x<4800$. The integer solutions to the inequality are $x=53$ and $x=54$.

If $x=53$, then $7788<100 y \leq 7888$ and $y=78$. But then $100 y+192 x=17976$, which contradicts the second inequality.

If $x=54$, then $7684<100 y \leq 7784$ and $y=77$. Then $100 y+192 x=18068$.

## Answer: a page costs 54 kopecks, and the cover costs 77 rubles