Question

Две бутылки А и В заполнены водой. Сначала 1/4 воды из А перелили в В, а затем 1/3 воды из В перелили в А, после чего количество воды в них сравнялось. Найдите первоначальное отношение количества воды в этих бутылках.

Answer 1

Пусть x - количество воды в А, y - в В. Уравнение: 
x-1/4x+1/3(y+1/4x)=y+1/4x-1/3(y+1/4x). 
Решаем - получаем x/y =1/2.
вот и все

Answer 2

Problem Analysis

We are given two bottles, A and B, filled with water. First, 1/4 of the water from bottle A is poured into bottle B. Then, 1/3 of the water from bottle B is poured back into bottle A. After these operations, the amount of water in both bottles becomes equal. We need to find the initial ratio of the amount of water in these bottles.

Solution

Let's assume that the initial amount of water in bottle A is x liters and the initial amount of water in bottle B is y liters.

According to the given information, the following operations are performed: 1. 1/4 of the water from bottle A is poured into bottle B. After this operation, the amount of water in bottle A becomes (3/4)x and the amount of water in bottle B becomes y + (1/4)x. 2. 1/3 of the water from bottle B is poured back into bottle A. After this operation, the amount of water in bottle A becomes (3/4)x + (1/3)(y + (1/4)x) and the amount of water in bottle B becomes y + (1/4)x - (1/3)(y + (1/4)x).

According to the problem, the amount of water in both bottles becomes equal after these operations. Therefore, we can set up the following equation:

(3/4)x + (1/3)(y + (1/4)x) = y + (1/4)x - (1/3)(y + (1/4)x)

Simplifying the equation, we get:

(3/4)x + (1/3)y + (1/12)x = y + (1/4)x - (1/3)y - (1/12)x

Combining like terms, we get:

(3/4 + 1/12)x - (1/3 - 1/3)y = y - (1/4)x

Simplifying further, we get:

(9/12 + 1/12)x = (4/4)y

(10/12)x = (4/4)y

(5/6)x = y

Therefore, the initial ratio of the amount of water in bottle A to bottle B is 5:6.

Answer

The initial ratio of the amount of water in bottles A and B is 5:6.