Question

В школе 1000 учащихся занимаются в различных школьных кружках и секциях. Кружков и секций, где занимается по 20 человек, в 10 раз меньше, чем тех, которые насчитывают в своем составе по 10 человек. В остальных кружках и секциях по 50 человек. Сколько кружков и секций в школе?

Answer 1

Кол-во детей в кружках по 50 чел кончается либо на 50 либо на 00.
Значит в кружках из 10 и 20 человек то же общее кол-во детей  кончается либо на 50 либо на 00, т.е. делится на 50
х-кол-во кружков из 20 детей, 20х-кол-во детей в этих кружках
10х-кол-во кружков из 10 детей, 10*10х=100х-кол-во детей в таких кружках

20х+100х=120х -делится на 50. Путем несложного перебора х=1,2,3,4,5 подходит х=5, 
т.е. в школе 5 кружков по 20 чел (всего там 5*20=100чел), 
5*10=50 кружков по 10 чел (всего там 50*10=500 чел), остальные 
1000-100-500=400 чел в кружках по 50 чел.
т.о. 400/50=8кружков по 50чел.
Всего 5+50+8=63 кружка.

Answer 2

Calculation of the Number of Clubs and Sections in the School

To calculate the number of clubs and sections in the school, we need to consider the following information:

- There are 1000 students in the school. - Some clubs and sections have 20 members. - Other clubs and sections have 10 members. - The clubs and sections with 20 members are 10 times fewer than those with 10 members. - The remaining clubs and sections have 50 members.

Let's break down the calculation step by step:

1. Calculate the number of clubs and sections with 20 members: - Let's assume the number of clubs and sections with 10 members is x. - According to the given information, the number of clubs and sections with 20 members is 10 times fewer than those with 10 members. Therefore, the number of clubs and sections with 20 members is x/10.

2. Calculate the number of clubs and sections with 10 members: - The total number of students in the school is 1000. - The number of students in each club or section with 10 members is 10. - Therefore, the number of clubs and sections with 10 members is 1000/10 = 100.

3. Calculate the number of clubs and sections with 20 members: - The number of clubs and sections with 20 members is x/10.

4. Calculate the number of clubs and sections with 50 members: - The remaining clubs and sections have 50 members. - The total number of students in the school is 1000. - The number of students in each club or section with 50 members is 50. - Therefore, the number of clubs and sections with 50 members is 1000/50 = 20.

5. Calculate the total number of clubs and sections: - The total number of clubs and sections is the sum of the clubs and sections with 10 members, clubs and sections with 20 members, and clubs and sections with 50 members. - Therefore, the total number of clubs and sections is 100 + (x/10) + 20.

Now, let's summarize the calculation:

- The total number of clubs and sections in the school is 100 + (x/10) + 20.

Please note that we don't have the exact value of x from the given information. If you have any specific value for x, we can substitute it into the calculation to find the exact number of clubs and sections in the school.