13.367. Several students decided to buy a tape recorder priced between 170 and 195 dollars. However, at the last moment, two of them refused to participate in the purchase, so each of the remaining had to contribute 1 dollar more. What was the price of the tape recorder?
Solution.

Let $x$ be the amount each student was originally supposed to contribute; $y$ be the number of students. According to the problem,
\[
\left\{
\begin{array}{l}
2 x = y - 2, \\
x y \geq 170, \\
x y \leq 195,
\end{array}
\right.
\left\{
\begin{array}{l}
x = \frac{y}{2} - 1, \\
y\left(\frac{y}{2} - 1\right) \geq 170, \\
y\left(\frac{y}{2} - 1\right) \leq 195 .
\end{array}
\right.
\]

Solving the inequalities, we find $y = 20$, then $x = \frac{20}{2} - 1 = 9$ (dollars), and the cost of the tape recorder is $x y = 180$ dollars.

Answer: 180 dollars.