Our three classes, a total of 84 students, went to the cinema. The ticket cost 50 Kč, but every 12th student had a 50% discount and every 35th student got in for free. How much did the entrance fee cost for all the students?

(M. Volfová)
Since $84: 12=7$, 7 students had a half-price ticket, i.e., a ticket for 25 Kč. Since $84: 35=2$ (remainder 14), 2 students had free entry. In total, the tickets cost

$$
7 \cdot 25+2 \cdot 0+(84-7-2) \cdot 50=175+0+75 \cdot 50=3925(\mathrm{~K} ̌) .
$$