85. The percentage of VII grade students attending gymnastics classes is between 2.9 and $3.1 \%$. Determine the smallest possible number of students in this class.
Solution. If there are $x$ students in the class and $y$ of them do gymnastics, then by the condition $2.9 < 100 \cdot \frac{y}{x} < 3.1$, or $29x < 1000y < 31x$. If $x \leqslant 32$, then $31x \leqslant 992 \leqslant 1000y$, so $x \geqslant 33$. Since $29 \cdot 33 < 1000 \cdot y < 31 \cdot 33$, the number of students sought is 33