Question

В двух рядах 30 спортсменов. Когда из первого ряда переставили во второй трёх спортсменов, то в каждом ряду стало одинаковое число спортсменов. Сколько спортсменов было в каждом ряду первоначально?

Answer 1

Если в двух рядах вместе 30 спортсменов, то когда стало поровну - в каждом ряду стало по 15 человек. Значит первоначально в 1 ряду было (15 + 3) = 18 спортсменов, а во 2 ряду (15 - 3) = 12 спортсменов.
Ответ: 18 и 12 спортсменов

Answer 2

Problem Analysis

We have two rows of sportsmen, and when three sportsmen are moved from the first row to the second row, the number of sportsmen in each row becomes the same. We need to determine the initial number of sportsmen in each row.

Solution

Let's assume that initially there were x sportsmen in the first row and y sportsmen in the second row.

According to the given information, when three sportsmen are moved from the first row to the second row, the number of sportsmen in each row becomes the same. Therefore, we can set up the following equation:

x - 3 = y + 3

Simplifying the equation, we get:

x - y = 6 ---(Equation 1)

We also know that the total number of sportsmen in both rows is 30. Therefore, we can set up another equation:

x + y = 30 ---(Equation 2)

Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From Equation 2, we can express x in terms of y:

x = 30 - y

Substituting this value of x into Equation 1, we get:

(30 - y) - y = 6

Simplifying the equation, we have:

30 - 2y = 6

Solving for y, we get:

2y = 30 - 6

2y = 24

y = 12

Substituting this value of y back into Equation 2, we can find the value of x:

x + 12 = 30

x = 30 - 12

x = 18

Therefore, the initial number of sportsmen in each row was 18 in the first row and 12 in the second row.

Answer

The initial number of sportsmen in each row was 18 in the first row and 12 in the second row.