Question

В двух бочках было 725 л бензина. Когда из первой бочки взяли 1/3 , а из второй бочки 2/7 бензина, то в обеих бочках бензина стало поровну. Сколько литров бензина было в каждой бочке первоначально?

Answer 1

Пусть во второй бочке х литров,

 тогда в первой бочке (725-х) литров.

 Из первой взяли 1/3, осталось 2/3 от (724-х),

Это равно 2/3*(725-x).

Из второй взяли 2/7,  осталось 5/7 от х. Это 5/7*x,  

Остатки равны.
2/3*(725-x)=5/7*x.

2/3*725-2/3*x=5/7*x.

 5/7*x+2/3*x=2*725/3.

29/21*x=2*725/3.
x=(2*725*21)/(3*29).

Сокращаем на 3 и на 29.

Получится х=350

Это во второй бочке,значит в первой 725-350=375.

Ответ: 375 л, 350 л.

Answer 2

Problem Analysis

We are given that there were 725 liters of gasoline in two barrels. When 1/3 of the gasoline was taken from the first barrel and 2/7 of the gasoline was taken from the second barrel, the remaining gasoline in both barrels was equal. We need to determine how many liters of gasoline were initially in each barrel.

Solution

Let's assume that the initial amount of gasoline in the first barrel is x liters. Therefore, the initial amount of gasoline in the second barrel would be (725 - x) liters.

According to the given information, when 1/3 of the gasoline is taken from the first barrel, the remaining amount of gasoline in the first barrel is (2/3)x liters. Similarly, when 2/7 of the gasoline is taken from the second barrel, the remaining amount of gasoline in the second barrel is (5/7)(725 - x) liters.

We are told that the remaining gasoline in both barrels is equal. Therefore, we can set up the following equation:

(2/3)x = (5/7)(725 - x)

To solve this equation, we can cross-multiply and simplify:

7(2/3)x = 3(5/7)(725 - x) 14x = 15(725 - x) 14x = 10875 - 15x 14x + 15x = 10875 29x = 10875 x = 375

Therefore, the initial amount of gasoline in the first barrel was 375 liters, and the initial amount of gasoline in the second barrel was 725 - 375 = 350 liters.

Answer

The initial amount of gasoline in each barrel was 375 liters and 350 liters, respectively.