Question

Сосуд емкостью 8 литров заполнили смесью кислорода и азота, причем на долю кислорода приходится16% емкости сосуда. Из этого сосоуда выпускают некоторое колличество смеси и дополняют сосуд до прежнего объема азотом и вновь выпускают такое же колличество смеси. После чего опять дополняют сосуд азотом до 8 литров, в результате в сосуде стало 9% кислорода.Сколько литров смеси выпускали из сосуда каждый раз?

Answer 1

сосуд емкостью 8 литров заполнили смесью кислорода и азота, причем на долю кислорода приходится16% емкости сосуда. Из этого сосоуда выпускают некоторое колличество смеси и дополняют сосуд до прежнего объема азотом и вновь выпускают такое же колличество смеси. После чего опять дополняют сосуд азотом до 8 литров, в результате в сосуде стало 9% кислорода.Сколько литров смеси выпускали из сосуда каждый раз?

8------100%

х-----16%

8*16\100=1,28 л было кисллорода

8-------100%

х------9%

8*9\100=0,02 литра

(1.28-0.02)\2=0,63 литра смеси выпускали из сосуда каждый раз

Answer 2

Problem Analysis

We have a vessel with a capacity of 8 liters filled with a mixture of oxygen and nitrogen. The oxygen occupies 16% of the vessel's capacity. Some amount of the mixture is released from the vessel, and then the vessel is refilled with nitrogen to its original volume. The same amount of the mixture is released again, and the vessel is refilled with nitrogen to its original volume. After this process, the vessel contains 9% oxygen. We need to determine how many liters of the mixture were released from the vessel each time.

Solution

Let's break down the problem step by step:

1. Initially, the vessel contains a mixture of oxygen and nitrogen. The oxygen occupies 16% of the vessel's capacity. This means that the vessel contains 0.16 * 8 = 1.28 liters of oxygen [[1]].

2. Some amount of the mixture is released from the vessel. Let's assume this amount is x liters.

3. After releasing x liters of the mixture, the vessel is refilled with nitrogen to its original volume of 8 liters. Since the vessel initially contained 1.28 liters of oxygen, the remaining volume after releasing x liters of the mixture is 8 - 1.28 = 6.72 liters.

4. The same amount of the mixture is released again, which is x liters.

5. After releasing x liters of the mixture for the second time, the vessel is refilled with nitrogen to its original volume of 8 liters. The remaining volume of oxygen in the vessel is now 6.72 - 1.28 = 5.44 liters.

6. Finally, the vessel is refilled with nitrogen to its original volume of 8 liters. The remaining volume of oxygen in the vessel is 8 - 5.44 = 2.56 liters.

7. After this process, the vessel contains 9% oxygen. This means that the vessel contains 0.09 * 8 = 0.72 liters of oxygen.

Now, we can set up an equation to solve for x:

2.56 - x = 0.72

Simplifying the equation:

x = 2.56 - 0.72 = 1.84 liters

Therefore, each time the vessel is released, 1.84 liters of the mixture are released.

Conclusion

Each time the vessel is released, 1.84 liters of the mixture are released.