Question

В двух бочках 725 литров бензина .когда из первой бочки взяли ⅓ ,а из второй бочки два седьмых (дробь) бензина , то в обеих бочках бензина стало поровну. Сколько литров бензина было в каждой бочке первоначально ????

Answer 1

Х - было в первой бочке, после  стало х*(1- 1/3)=2/3х
(725 - х) - во второй бочке, после  стало (725-х)*5/7 
2/3х=(725-х)*5/7
14х=10875 -15х
29х=10875
х=10875 / 29 
х=375 - в первой бочке
725-375=350 - во второй бочке

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 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: - 1/3 of the gasoline is taken from the first barrel, which means the remaining amount in the first barrel is (2/3)x liters. - 2/7 of the gasoline is taken from the second barrel, which means the remaining amount in the second barrel is (5/7)y liters.

It is also mentioned that the remaining gasoline in both barrels is equal. Therefore, we can set up the following equation:

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

To solve this equation, we can cross-multiply:

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

Simplifying, we get:

(14/3)x = (25/7)y

To make the equation easier to work with, we can multiply both sides by 3 and 7 to eliminate the fractions:

14x = 75y

Now, we can solve for x in terms of y:

x = (75/14)y

Since we are looking for the initial amount of gasoline in each barrel, x and y should be positive integers. To find the values of x and y that satisfy this condition, we can try different values of y and calculate the corresponding value of x.

Let's start by assuming y = 1 liter. Substituting this into the equation, we get:

x = (75/14) * 1 = 75/14 ≈ 5.36 liters

Since x should be a positive integer, y = 1 is not a valid solution.

Let's try y = 2 liters:

x = (75/14) * 2 = 150/14 ≈ 10.71 liters

Again, x is not a positive integer.

Let's try y = 3 liters:

x = (75/14) * 3 = 225/14 ≈ 16.07 liters

Once again, x is not a positive integer.

We can continue this process and try different values of y until we find a valid solution.

Calculation

Let's try y = 4 liters:

x = (75/14) * 4 = 300/14 ≈ 21.43 liters

This time, x is not a positive integer.

Let's try y = 5 liters:

x = (75/14) * 5 = 375/14 ≈ 26.79 liters

Again, x is not a positive integer.

Let's try y = 6 liters:

x = (75/14) * 6 = 450/14 ≈ 32.14 liters

Once again, x is not a positive integer.

Let's try y = 7 liters:

x = (75/14) * 7 = 525/14 ≈ 37.50 liters

This time, x is not a positive integer.

Let's try y = 8 liters:

x = (75/14) * 8 = 600/14 ≈ 42.86 liters

Again, x is not a positive integer.

Let's try y = 9 liters:

x = (75/14) * 9 = 675/14 ≈ 48.21 liters

Once again, x is not a positive integer.

Let's try y = 10 liters:

x = (75/14) * 10 = 750/14 ≈ 53.57 liters

This time, x is not a positive integer.

Let's try y = 11 liters:

x = (75/14) * 11 = 825/14 ≈ 58.93 liters

Again, x is not a positive integer.

Let's try y = 12 liters:

x = (75/14) * 12 = 900/14 ≈ 64.29 liters

Once again, x is not a positive integer.

Let's try y = 13 liters:

x = (75/14) * 13 = 975/14 ≈ 69.64 liters

This time, x is not a positive integer.

Let's try y = 14 liters:

x = (75/14) * 14 = 1050/14 = 75 liters

Finally, we have found a valid solution where x and y are positive integers. Therefore, the initial amount of gasoline in each barrel was 75 liters.

Answer

The initial amount of gasoline in each barrel was 75 liters.