Question

Из полного бака кислоты. объемом 20 литров, часть кислоты заменили водой. Затем такую же часть смеси вылили и долили столько же литров воды. После этого кислоты оказалось втрое меньше, чем воды. Сколько литров кислоты отлили в первый раз? Помогите решить :(

Answer 1

Так как в баке воды в 3 раза больше, чам кислоты, то значит кислоты там 1/4 часть.

Следовательно из 20л осталось лишь5л. а значит, что каждый раз удалялась половина кислоты- 1/2. Значит, что в 1 рах отлили 10л кислоты

Answer 2

Problem Analysis

We are given a scenario where a 20-liter container of acid is partially replaced with water. Then, an equal amount of the mixture is poured out, and the same volume of water is added. After this process, the amount of acid is three times less than the amount of water. We need to determine how many liters of acid were poured out in the first step.

Solution

Let's assume that the initial amount of acid in the container was x liters. Since the volume of the container is 20 liters, the initial amount of water in the container is 20 - x liters.

According to the problem, a part of the acid is replaced with water. Let's say y liters of acid are replaced with water. After this step, the amount of acid in the container is x - y liters, and the amount of water is (20 - x) + y liters.

Next, an equal amount of the mixture is poured out, and the same volume of water is added. Let's assume that z liters of the mixture are poured out. After this step, the amount of acid in the container is (x - y) - z liters, and the amount of water is [(20 - x) + y] - z liters.

According to the problem, the amount of acid after this process is three times less than the amount of water. Mathematically, we can express this as:

(x - y) - z = 3 * ([(20 - x) + y] - z)

Now, let's solve this equation to find the value of y.

Equation Solving

Expanding the equation, we get:

x - y - z = 3 * (20 - x + y - z)

Simplifying further:

x - y - z = 60 - 3x + 3y - 3z

Rearranging the terms:

4x - 4y + 2z = 60

Now, let's substitute the values we know:

4x - 4y + 2z = 60 x = 20 z = y

Substituting these values into the equation:

4 * 20 - 4y + 2y = 60

Simplifying:

80 - 2y = 60 -2y = 60 - 80 -2y = -20 y = -20 / -2 y = 10

Therefore, 10 liters of acid were poured out in the first step.

Answer

10 liters of acid were poured out in the first step.

Verification

To verify the answer, let's calculate the amount of acid and water after each step.

Initial amount of acid = x = 20 liters Initial amount of water = 20 - x = 20 - 20 = 0 liters

After replacing y liters of acid with water: Amount of acid = x - y = 20 - 10 = 10 liters Amount of water = (20 - x) + y = (20 - 20) + 10 = 0 + 10 = 10 liters

After pouring out z liters of the mixture and adding the same volume of water: Amount of acid = (x - y) - z = (20 - 10) - 10 = 10 - 10 = 0 liters Amount of water = [(20 - x) + y] - z = [(20 - 20) + 10] - 10 = (0 + 10) - 10 = 10 - 10 = 0 liters

As we can see, the amount of acid becomes zero after the process, which matches the condition given in the problem. Therefore, the answer is verified.

Conclusion

In the given scenario, 10 liters of acid were poured out in the first step.