3. The price of one pencil is a whole number of denars. The price of 9 such pencils is greater than 1100 denars, but less than 1200 denars. The price of 13 pencils is greater than 1500 denars, but less than 1600 denars. How much does one pencil cost?
Solution. Let $x$ be the price of one pencil. According to the problem, $x$ is an integer in denars. According to the given conditions, we have

$$
\begin{aligned}
& 1100<9 x<1200 \\
& 1500<13 x<1600
\end{aligned} \Rightarrow \begin{aligned}
& 122<x<134 \\
& 115<x<124
\end{aligned}
$$

where, in the first inequality, we divide by 9, and in the second by 13. If we arrange the last two inequalities, we get:

$$
115<122<x<124<134
$$

which means that $x=123$. Therefore, the price of one pencil is 123 denars.