Question

В спортивной школе есть секция шахмат и секция настольного тенниса. Каждый ученик спортивной школы ходит либо на секцию шахмат, либо на секцию настольного тенниса. Каждый шахматист дружит с тремя теннисистами, а каждый теннисист — с пятью шахматистами. Сколько всего учеников в спортивной школе, если известно, что шахматистов больше , а теннисистов меньше ?

Answer 1

Возможно 240 , из них 150 шахматистов и 90 теннисистов, но здесь непонятно скажем 1 шахматист дружит с теннисистами только 1 раз или несколькими подряд?

Answer 2

#### Problem Analysis We are given that there is a sports school with two sections: chess and table tennis. Each student in the sports school attends either the chess section or the table tennis section. Additionally, each chess player is friends with three table tennis players, and each table tennis player is friends with five chess players. We need to determine the total number of students in the sports school, given that there are more chess players than table tennis players. #### Solution Let's assume there are **C** chess players and **T** table tennis players in the sports school. We know that each chess player is friends with three table tennis players, so the total number of friendships between chess players and table tennis players is **3C**. Similarly, each table tennis player is friends with five chess players, so the total number of friendships between table tennis players and chess players is **5T**. Since each friendship is counted twice (once for each person involved), the total number of friendships can be calculated as **3C + 5T**. We also know that there are more chess players than table tennis players, so we can write the following inequality: **C > T**. To find the total number of students in the sports school, we need to add the number of chess players and table tennis players: **C + T**. To solve this problem, we need to find the values of **C** and **T** that satisfy the given conditions. #### Solution Steps 1. Start with the inequality **C > T**. 2. Substitute the total number of friendships into the inequality: **3C + 5T > 0**. 3. Simplify the inequality: **3C > -5T**. 4. Divide both sides of the inequality by 3 (since 3 is positive): **C > (-5/3)T**. 5. Since the number of students cannot be negative, we can assume that **T = 1** (the minimum possible value for T). 6. Substitute **T = 1** into the inequality: **C > (-5/3)(1)**. 7. Simplify the inequality: **C > -5/3**. 8. Since the number of students cannot be fractional, we can assume that **C = 0** (the minimum possible value for C). 9. Substitute **C = 0** into the inequality: **0 > T**. 10. The only integer value that satisfies the inequality is **T = 0**. 11. Therefore, the minimum possible values for C and T are **C = 0** and **T = 0**. 12. The total number of students in the sports school is **C + T = 0 + 0 = 0**. #### Answer Therefore, the total number of students in the sports school is **0**. Please let me know if you need any further clarification.