Question

Задача: В двух бочках 725 л. бензина. Когда из первой бочки взяли 1\3,а из второй 2\7 бензина, то в обоих бочках стало поровну. Сколько бензина было в каждой бочке? Уравнения: 8y=-62,4+5y x+3/7=2x-1/5Заранее спасибо!

Answer 1

Пусть в первой бочке х литров, тогда во второй 725-х. После того как из первой взяли 1/3 в бочке осталось (2х)/3 литров.
После того как из второй бочки взяли 2/7 литров бензина в ней осталось 5/7(725-х)
Получаем уравнение:  
(2х)/3=5/7(725-х)
(2х)/3=3625/7-(5х)/7
(2х)/3+(5х)/7=3625/7
(29х)/21=3625/7
(29х)/21-3625/7=0
(29х)/21-(3625*3)/(7*3)=0
(29х-10875)/21=0
29х-10875=0
29х=10875
х=10875/29
х=375  

В первой бочке было 375 л. бензина
Во второй бочке было 725-375=350 л. бензина  

Уравнения:
8y=-62,4+5y
8у-5у=-62,4
3у=-62,4
у=-62,4/3
у=-20,8

x+3/7=2x-1/5
х-2х=-1/5 – 3/7
-х=-22/35
х=22/35

Answer 2

Problem:

The problem states that there are two barrels with a total of 725 liters of gasoline. When 1/3 of the gasoline is taken from the first barrel and 2/7 of the gasoline is taken from the second barrel, the amount of gasoline in both barrels becomes equal. The task is to determine how much gasoline was initially in each barrel.

Solution:

Let's assume that the amount of gasoline in the first barrel is x liters and the amount of gasoline in the second barrel is y liters.

According to the problem, the following equations can be set up:

Equation 1: Taking 1/3 of the gasoline from the first barrel and 2/7 of the gasoline from the second barrel results in an equal amount of gasoline in both barrels. ``` x - (1/3)x = y - (2/7)y ```

Equation 2: The total amount of gasoline in both barrels is 725 liters. ``` x + y = 725 ```

To solve this system of equations, we can use the given equations and solve for x and y.

Solution Steps:

Step 1: Simplify Equation 1 by multiplying both sides by the least common denominator (LCD) of 3 and 7, which is 21. ``` 21x/3 - 7x/3 = 21y/7 - 6y/7 7x - 7x/3 = 3y - 2y/7 ```

Step 2: Simplify Equation 2. ``` x + y = 725 ```

Step 3: Combine like terms in Equation 1. ``` (21x - 7x)/3 = (3y - 2y)/7 14x/3 = y/7 ```

Step 4: Solve for y in terms of x using Equation 3. ``` y = (14x/3) * 7 y = 98x/3 ```

Step 5: Substitute the value of y from Equation 4 into Equation 2. ``` x + 98x/3 = 725 ```

Step 6: Solve for x. ``` 3x + 98x = 2175 101x = 2175 x = 2175/101 ```

Step 7: Substitute the value of x from Equation 6 into Equation 4 to solve for y. ``` y = (98 * (2175/101))/3 ```

Therefore, the amount of gasoline in each barrel is approximately 21.53 liters in the first barrel and 503.47 liters in the second barrel.

Please note that the given equations provided in the question do not seem to be relevant to solving the problem. The solution provided above is based on the problem statement and the equations derived from it.