1. In a school, there are 300 students, and each is engaged in one winter and one summer sport. During the summer, 60% of them play football, and the remaining $40 \%$ swim. In the winter, students either ski or play hockey, but not both sports simultaneously. $56 \%$ of those who play football in the summer ski in the winter, and $30 \%$ of the football players play hockey in the winter. Determine how many students swim and play hockey.
Solution. In the summer, 180 students play football, and 120 swim. Of the football players, $30\%$ play hockey in the winter, i.e., $\frac{30 \times 180}{100}=54$ students. Therefore, the remaining $180-54=126$ students who play football ski in the winter. If we denote the total number of students who ski in the winter by $x$, then $\frac{56 x}{100}=126$, so $x=225$. According to this, 75 students play hockey in the winter. Since 54 students play both football and hockey, 21 students remain who are involved in swimming and hockey.