Question

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

Answer 1

пусть в 1-й бочке первоначально было х л бензина, тогда во 2-й 725 - х. когда из первой бочки взяли1/3 бензина, то в ней осталось 1-1/3 = 2/3бензина, а во 2-й 1 - 2/7= 5/7 бензина. 
2/3х = 5/7(725 - х) 
(затем нам надо убрать дроби, и поэтому умножаем обе части на 21) 
21* 2/3х =21*5/7(725 - х) 
14х = 15*725-15х 
14х+ 15х=10875 
29х=10875 
х=10875:29 
х=375 
375(л) - было первоначально в 1-й бочке 
725 - 375= 350(л) - было первоначально во 2-й бочке. 
ответ: 375 л, 350 л

Answer 2

Problem Analysis

We are given two barrels with a total capacity of 725 liters of gasoline. After taking 1/3 of the gasoline from the first barrel and 2/7 of the gasoline from the second barrel, the remaining 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 and in the second barrel is y liters.

According to the given information, we can set up the following equations:

Equation 1: After taking 1/3 of the gasoline from the first barrel, the remaining gasoline is (2/3)x liters. Equation 2: After taking 2/7 of the gasoline from the second barrel, the remaining gasoline is (5/7)y liters. Equation 3: The remaining gasoline in both barrels is equal.

From Equation 1 and Equation 2, we can write:

(2/3)x = (5/7)y

Simplifying this equation, we get:

14x = 15y

Now, let's use Equation 3 to set up another equation:

(2/3)x + (5/7)y = 725

To solve these equations, we can use substitution or elimination method. Let's use the elimination method.

Multiplying Equation 1 by 15 and Equation 2 by 14, we get:

30x = 35y

Now, subtracting Equation 2 from Equation 1, we get:

30x - 35y = 0

Substituting this value in Equation 3, we get:

0 + (5/7)y = 725

Simplifying this equation, we get:

y = (7/5) * 725

Calculating the value of y, we find:

y = 1015 liters

Substituting this value in Equation 1, we can find the value of x:

(2/3)x = (5/7) * 1015

Simplifying this equation, we get:

(2/3)x = 725

Calculating the value of x, we find:

x = (3/2) * 725

x = 1087.5 liters

Therefore, the initial amount of gasoline in the first barrel was 1087.5 liters and in the second barrel was 1015 liters.

Answer

The initial amount of gasoline in each barrel was 1087.5 liters and 1015 liters, respectively.