Help please

A bottle containing 10 liters of alcohol one liter of alcohol is removed and replaced with water. After a liter of the mixture was removed and replaced with water, the operation being carried out 7 times in total. Then that amount of alcohol remains in the container.

I just did that

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To find out how much alcohol remains in the container after multiple replacements, we need to understand the concept of concentration and apply it to each step of the process.

Let's break down the steps and calculate the concentration at each stage:

1. Initially, we have a bottle containing 10 liters of alcohol. So, the concentration of alcohol is 10/10 = 1.

2. After the first replacement, 1 liter of alcohol is removed and replaced with water. So, there are 9 liters of alcohol left in the bottle. However, the total volume remains the same at 10 liters. Therefore, the concentration of alcohol is 9/10.

3. In the second replacement, 1 liter of the mixture (alcohol + water) is removed and replaced with water. At this stage, we have 9 liters of the mixture, but we need to calculate the concentration. Since the concentration in step 2 was 9/10, when 1 liter of water (with concentration 0/1) is added, we have:

(9/10) * (1 - 1/10) + (0/1) * (1/10) = 81/100

Therefore, the concentration of alcohol after the second replacement is 81/100.

4. We repeat the above calculation for each subsequent replacement, keeping track of the concentration at each step. The concentration of alcohol after the third replacement would be (81/100) * (1 - 1/10) + (0/1) * (1/10) = 729/1000.

5. Following this process, continue calculating the concentration after each replacement until the seventh replacement.

At the end of the seventh replacement, you will have the final concentration of alcohol in the bottle. To find the amount of alcohol remaining in the container, multiply the final concentration by the total volume of the mixture, which is 10 liters.