Question

В одном зале кинотеатра в 4 раза больше зрителей,чем в другом. Если из первого зала уйдут 102 человека, а во второй придут 48,то зрителей в обоих залах будет поровну.Сколько зрителей в каждом зале? ДАЮ 50 БАЛЛОВ. РЕШИТЕ ПОЖАЛУСТА

Answer 1

Пусть в другом зале было х человек, тогда в первом - 4х человек. Т.к если из первого зала уйдут 102 человека, а во второй придут 48, и зрителей в обоих залах будет поровну, то составим уравнение:
4х - 102 = х + 48
4х - 102 - х - 48 = 0
3х - 150 = 0
3х = 150
х = 50
Во втором зале 50 человек, в первом - 200 человек.
ОТВЕТ: 50 чел ; 200 чел

Answer 2

Problem Analysis

We are given that there are four times as many spectators in one cinema hall as in another. If 102 people leave the first hall and 48 people enter the second hall, the number of spectators in both halls will be equal. We need to find the number of spectators in each hall.

Solution

Let's assume the number of spectators in the first hall is x. According to the problem, there are four times as many spectators in the first hall as in the second hall. Therefore, the number of spectators in the second hall is x/4.

If 102 people leave the first hall, the number of spectators in the first hall becomes x - 102. If 48 people enter the second hall, the number of spectators in the second hall becomes (x/4) + 48.

According to the problem, the number of spectators in both halls will be equal after these changes. Therefore, we can set up the following equation:

(x - 102) = (x/4) + 48

Now, let's solve this equation to find the value of x.

Equation Solving

To solve the equation, we can start by simplifying it:

(x - 102) = (x/4) + 48

Multiplying both sides of the equation by 4 to eliminate the fraction:

4(x - 102) = x + 192

Expanding the equation:

4x - 408 = x + 192

Moving all the terms with x to one side of the equation:

4x - x = 192 + 408

Simplifying:

3x = 600

Dividing both sides of the equation by 3:

x = 200

Answer

Therefore, there are 200 spectators in the first hall and 200/4 = 50 spectators in the second hall.

So, there are 200 spectators in the first hall and 50 spectators in the second hall.