Question

В двух бидонах было 51 л молока.После того как из первого бидона отлили 16,2 л,а из второго 7,2 л,во втором бидоне молока окозалось в 4 раза больше,чем в первом.Сколько литров молока было в каждом бидоне первоночольно?

Answer 1

Пусть х литров было в первом бидоне, а у - во втором. Известно, что в обоих бидонах было 51 литров молока.
Известно, что когда из первого бидона отлили 16,2 литра (х - 16,2 - осталось), а из второго - 7,2 литра (у - 7,2 - осталось), во втором бидоне молока оказалось в 4 раза больше, чем в первом.

Составляю систему уравнений:

$\left \{ {{x+y=51} \atop {4(x-16,2)=y-7,2}} \right.$   $\left \{ {{y=51-x} \atop {4(x-16,2)=51-x-7,2}} \right.$

Решаем второе уравнение системы:
4(х - 16,2) = 51 - х - 7,2
4х - 64,8 = 43,8 - х
4х + х = 43,8 + 64,8
5х = 108,6
х = 21,72
1) 21,72 (л) - было в первом бидоне
2) 51 - 21,72 = 29,28 (л) - было во втором бидоне

Ответ: 21,72; 29,28

Answer 2

Problem Analysis

We are given two containers of milk. After pouring out 16.2 liters from the first container and 7.2 liters from the second container, the amount of milk in the second container is four times greater than the amount in the first container. We need to determine the initial amount of milk in each container.

Solution

Let's assume the initial amount of milk in the first container is x liters. Since 16.2 liters were poured out, the remaining amount of milk in the first container is x - 16.2 liters.

Similarly, let's assume the initial amount of milk in the second container is y liters. Since 7.2 liters were poured out, the remaining amount of milk in the second container is y - 7.2 liters.

According to the given information, the amount of milk in the second container is four times greater than the amount in the first container. This can be expressed as:

(y - 7.2) = 4(x - 16.2)

Now, we can solve this equation to find the values of x and y.

Calculation

Let's solve the equation:

(y - 7.2) = 4(x - 16.2)

Expanding the equation:

y - 7.2 = 4x - 64.8

Rearranging the equation:

4x - y = 57.6 ---(1)

We also know that the total amount of milk in both containers is 51 liters:

x + y = 51 ---(2)

Now, we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Using equation (2), we can express x in terms of y:

x = 51 - y

Substituting this value of x in equation (1):

4(51 - y) - y = 57.6

Simplifying the equation:

204 - 4y - y = 57.6

204 - 5y = 57.6

-5y = 57.6 - 204

-5y = -146.4

Dividing both sides by -5:

y = -146.4 / -5

y = 29.28

Substituting this value of y in equation (2):

x + 29.28 = 51

x = 51 - 29.28

x = 21.72

Answer

The initial amount of milk in the first container was 21.72 liters, and the initial amount of milk in the second container was 29.28 liters.

Verification

Let's verify our answer by checking if the given conditions are satisfied.

1. After pouring out 16.2 liters from the first container, the remaining amount of milk is 21.72 - 16.2 = 5.52 liters. 2. After pouring out 7.2 liters from the second container, the remaining amount of milk is 29.28 - 7.2 = 22.08 liters. 3. The amount of milk in the second container is four times greater than the amount in the first container: 22.08 = 4(5.52).

Therefore, our answer is verified.

Conclusion

The initial amount of milk in the first container was 21.72 liters, and the initial amount of milk in the second container was 29.28 liters.