Question

Нужно решить в ближайшее время!!! В двух бочках 725 литров бензина. когда из первой бочки взяли 1/3 (одну треть), а из второй 2/7 (две седьмых) бензина, то в обеих бочках бензина стало поровну. Сколько литров бензина было в каждой бочке первоначально?Просьба решить с пояснениями.

Answer 1

2/3х=5/7*(725-х)

Домножаем обе части на 21:

21*2/3х=21*7/5*(725-x)

14х+15х=15*725

29х=10875

х=10875:29

х=375л бензина-было в первой бочке.

725-375=350л бензина-было во второй бочке.

ОТВЕТ: 375л, 350л.

 

Answer 2

Решение задачи с бензином в бочках

Давайте рассмотрим эту задачу пошагово.

1. Обозначения: - Пусть x - количество бензина в первой бочке (в литрах). - Пусть y - количество бензина во второй бочке (в литрах).

2. Условие: - Из первой бочки взяли 1/3 бензина. - Из второй бочки взяли 2/7 бензина. - После взятия бензина из обеих бочек в них осталось одинаковое количество#### Problem Analysis We are given two barrels of gasoline, each with a capacity of 725 liters. After taking 1/3 of the gasoline from the first barrel and 2/7 of the gasoline from the second barrel, the amount of gasoline in both barrels becomes 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, after taking 1/3 of the gasoline from the first barrel, the remaining amount of gasoline in the first barrel is (2/3)x liters. Similarly, after taking 2/7 of the gasoline from the second barrel, the remaining amount of gasoline in the second barrel is (5/7)y liters.

We are also told that the remaining amount of 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 multiply both sides by the least common multiple (LCM) of 3 and 7, which is 21:

21 * (2/3)x = 21 * (5/7)y

Simplifying the equation:

14x = 15y

Now, we need to find the values of x and y that satisfy this equation and also ensure that the total amount of gasoline in both barrels is 725 liters.

We can start by assuming a value for x and then calculate the corresponding value of y using the equation. If the calculated value of y is an integer and the total amount of gasoline in both barrels is 725 liters, then we have found the solution.

Let's try different values of x and check if they satisfy the conditions:

1. If we assume x = 100 liters, then the equation becomes: 14 * 100 = 15y 1400 = 15y y = 1400 / 15 = 93.33 liters

The calculated value of y is not an integer, so this assumption does not satisfy the conditions.

2. If we assume x = 200 liters, then the equation becomes: 14 * 200 = 15y 2800 = 15y y = 2800 / 15 = 186.67 liters

The calculated value of y is not an integer, so this assumption does not satisfy the conditions.

3. If we assume x = 300 liters, then the equation becomes: 14 * 300 = 15y 4200 = 15y y = 4200 / 15 = 280 liters

The calculated value of y is an integer, but the total amount of gasoline in both barrels is 300 + 280 = 580 liters, which is less than 725 liters. So, this assumption does not satisfy the conditions.

4. If we assume x = 400 liters, then the equation becomes: 14 * 400 = 15y 5600 = 15y y = 5600 / 15 = 373.33 liters

The calculated value of y is not an integer, so this assumption does not satisfy the conditions.

5. If we assume x = 500 liters, then the equation becomes: 14 * 500 = 15y 7000 = 15y y = 7000 / 15 = 466.67 liters

The calculated value of y is not an integer, so this assumption does not satisfy the conditions.

6. If we assume x = 600 liters, then the equation becomes: 14 * 600 = 15y 8400 = 15y y = 8400 / 15 = 560 liters

The calculated value of y is an integer, and the total amount of gasoline in both barrels is 600 + 560 = 1160 liters, which is greater than 725 liters. So, this assumption does not satisfy the conditions.

7. If we assume x = 700 liters, then the equation becomes: 14 * 700 = 15y 9800 = 15y y = 9800 / 15 = 653.33 liters

The calculated value of y is not an integer, so this assumption does not satisfy the conditions.

8. If we assume x = 725 liters, then the equation becomes: 14 * 725 = 15y 10150 = 15y y = 10150 / 15 = 676.67 liters

The calculated value of y is not an integer, so this assumption does not satisfy the conditions.

From the above analysis, we can see that none of the assumptions satisfy the conditions. It seems that there is no solution that satisfies the given conditions.

Therefore, we cannot determine the initial amount of gasoline in each barrel based on the given information.

Conclusion: Based on the given information, it is not possible to determine the initial amount of gasoline in each barrel.