Question

В двух комнатах было 56 человек. когда в первую пришли ещё 12 человек, а во вторую 8 человек, то в комнатах стало поровну. сколько человек было в каждой комнате первоначально?

Answer 1

56:2=28    28-12=16    28-8=20

Answer 2

Problem Analysis

We are given that there were 56 people in two rooms. When 12 more people entered the first room and 8 more people entered the second room, the number of people became equal in both rooms. We need to determine the initial number of people in each room.

Solution

Let's assume that the initial number of people in the first room is x and the initial number of people in the second room is y.

According to the given information, we can set up the following equation: x + 12 = y - 8

Simplifying the equation, we get: x - y = -20

We also know that the total number of people in both rooms is 56. So we can set up another equation: x + y = 56

Now we have a system of two equations with two variables. We can solve this system 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 elimination.

Adding the two equations together, we get: (x - y) + (x + y) = -20 + 56 2x = 36 x = 18

Substituting the value of x into one of the equations, we can solve for y: 18 + y = 56 y = 56 - 18 y = 38

Answer

The initial number of people in the first room was 18, and the initial number of people in the second room was 38.

Please let me know if you need any further assistance!