Question

В двух бочках 725 л бензина. Когда из первой взяли 1/3 бензина(НЕ ЛИТРОВ), а из второй 2/7, то в обеих бочках стало бензина поровну. Сколько литров бензина было в каждой бочке первоначально. РАСПИШИТЕ ВСЁ ПОДРОБНО.

Answer 1

Пусть первоначально в первой бочке было х литров , после изменений стало х*(1-1/3) 
Тогда во второй бочке первоначально было (725-х) , а после изменений стало (725 - х) * (1-2/7)= (725 - х) * 5/7
Составим уравнение и решим его: 
х*2/3=(725-х)*5/7
14х=725*15-15х
29х=725*15
х=375 -  было в первой бочке
725-375=350 - было во второй бочке

Answer 2

Problem Analysis

We are given two barrels with a total of 725 liters of gasoline. 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, both barrels have an equal amount of gasoline. 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 is 725 - x liters.

From the first barrel, 1/3 of the gasoline is taken, which leaves 2/3 of the gasoline in the first barrel. Therefore, the amount of gasoline left in the first barrel is (2/3)x liters.

From the second barrel, 2/7 of the gasoline is taken, which leaves 5/7 of the gasoline in the second barrel. Therefore, the amount of gasoline left in the second barrel is (5/7)(725 - x) liters.

According to the problem, the amount of gasoline left in both barrels is the same. Therefore, we can set up the following equation:

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

Now, let's solve this equation to find the value of x.

Equation Solving

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

2x = (15/7)(725 - x)

Next, we can distribute the fraction on the right side:

2x = (15/7)(725) - (15/7)x

Now, let's simplify the equation:

2x + (15/7)x = (15/7)(725)

Combining like terms:

(29/7)x = (15/7)(725)

Finally, we can solve for x by dividing both sides by (29/7):

x = (15/7)(725) / (29/7)

Simplifying further:

x = 375

Therefore, the initial amount of gasoline in the first barrel is 375 liters.

To find the initial amount of gasoline in the second barrel, we can subtract this value from the total amount of gasoline:

725 - 375 = 350

Therefore, the initial amount of gasoline in the second barrel is 350 liters.

Answer

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