Question

Даю 100 баллов, срочно решите) В двух залах музея было 54 человека. Когда в первый зал пришли ещё 9 человек, а во второй- 7 человек, то в залах людей стало поровну. Сколько человек было в каждом зале первоначально?

Answer 1

1) 9+7=16(ч.)-пришли
2)54+16=70(ч.)-стало в 2-х залах
3)70:2=35(ч.)-стало в каждом зале
4) 35-9=26(ч.)-было в первом зале сначала
5) 35-7=28(ч.)-было во втором зале сначала

Ответ:26 и 28 человек.

уравнением так
х-было в первом зале сначала
у-было во втором зале сначала
х+у=54

х+9-стало в первом зале
у+7-стало во втором зале
х+9=у+7

Получаем систему
$\left \{ {{x+y=54} \atop {x+9=y+7}} \right. \\ \\ \left \{ {{x+y=54} \atop {x-y=7-9}} \right. \\ \\ \left \{ {{x+y=54 \atop {x-y=-2}} \right. \\ \\ 2x=54-2 \\ 2x=52 \\ \\ x=26 \\ y=28$

Ответ:26 и 28 человек первоначально.

Answer 2

Problem Analysis

To solve this problem, we need to determine the initial number of people in each of the two museum halls. We are given that there were initially 54 people in the two halls combined. When 9 more people entered the first hall and 7 more people entered the second hall, the number of people in each hall became equal.

Let's assume that the initial number of people in the first hall was x, and the initial number of people in the second hall was y.

Solution

1. We know that the total number of people in the two halls combined was 54. Therefore, we can write the equation: x + y = 54. 2. We are also given that when 9 more people entered the first hall and 7 more people entered the second hall, the number of people in each hall became equal. This can be represented by the equation: (x + 9) = (y + 7).

3. We can solve this system of equations to find the values of x and y.

- Rearrange the second equation to isolate x: x = y + 7 - 9 = y - 2.

- Substitute the value of x from the second equation into the first equation: (y - 2) + y = 54.

- Simplify the equation: 2y - 2 = 54.

- Add 2 to both sides of the equation: 2y = 56.

- Divide both sides of the equation by 2: y = 28.

4. Substitute the value of y back into the first equation to find x: x + 28 = 54.

- Subtract 28 from both sides of the equation: x = 54 - 28 = 26.

Answer

Therefore, the initial number of people in the first hall was 26, and the initial number of people in the second hall was 28.

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