Question

В двух бочках 725 литров 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 two barrels of gasoline, each with a capacity of 725 liters. From the first barrel, 1/3 of the gasoline is taken, and from the second barrel, 2/7 of the gasoline is taken. After this, the amount of gasoline in both barrels is equal. We need to determine the initial amount of gasoline 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.

Since the remaining amount of gasoline in both barrels is equal, we can set up the following equation:

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

Let's solve this equation to find the value of x.

Calculation

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

Multiplying both sides by 3 and 7 to eliminate the fractions:

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

14x = 15(725 - x)

14x = 10875 - 15x

14x + 15x = 10875

29x = 10875

x = 375

Answer

The initial amount of gasoline in the first barrel was 375 liters, and the initial amount of gasoline in the second barrel was 350 liters.

Explanation

Initially, the first barrel had 375 liters of gasoline, and the second barrel had 350 liters of gasoline. When 1/3 of the gasoline (125 liters) is taken from the first barrel, it is left with 250 liters. Similarly, when 2/7 of the gasoline (100 liters) is taken from the second barrel, it is left with 250 liters as well. Therefore, the amount of gasoline in both barrels becomes equal.