Question

В двух вагонах поезда ехало поровну пассажиров. После того, как с первого вагона вышло 7 пассажиров а со второго 21 пассажир во втором вагоне осталось в 3 раза меньше чем в другом. Сколько пассажиров было в каждом вагоне сначала？

Answer 1

Пусть в каждом вагоне первоначально было n пассажиров.
Тогда в I вагоне осталось   (n-7)  пассажиров,
а во II вагоне  (n - 21) пассажиров.
Зная, что во II вагоне осталось в  3 раза меньше пассажиров, составим уравнение:
$\frac{n-7}{n-21}= 3 \\ n-21 \neq 0 \\ n \neq 21 \\ \\ n - 7 = 3*(n-21) \\ n-7= 3n - 3*21 \\ n - 7 = 3n -63 \\ -7 + 63 = 3n - n \\ 2n = 56 \\ n = 56 : 2$
n= 28 (пассажиров) первоначально было в каждом вагоне
Проверим:
(28 - 7 )  / ( 28-21 ) = 21/7 =  3 (раза)

Ответ:  28 пассажиров было в каждом вагоне сначала.

Answer 2

Problem Analysis

We are given that there were an equal number of passengers in two train cars. After 7 passengers got off the first car and 21 passengers got off the second car, there were three times fewer passengers in the second car compared to the first car. We need to determine the initial number of passengers in each car.

Solution

Let's assume that the initial number of passengers in each car is x.

According to the given information, after 7 passengers got off the first car, the number of passengers remaining in the first car is x - 7. Similarly, after 21 passengers got off the second car, the number of passengers remaining in the second car is x - 21.

We are also given that the number of passengers remaining in the second car is three times fewer than the number of passengers remaining in the first car. Mathematically, we can represent this as:

(x - 21) = (x - 7) / 3

To solve this equation, we can start by multiplying both sides by 3 to eliminate the fraction:

3(x - 21) = x - 7

Expanding the equation:

3x - 63 = x - 7

Next, we can simplify the equation by combining like terms:

3x - x = 63 - 7

Simplifying further:

2x = 56

Finally, we can solve for x by dividing both sides of the equation by 2:

x = 28

Therefore, the initial number of passengers in each car was 28.

Answer

The initial number of passengers in each train car was 28.