The radiator of a car contains 20 liters of water. Five liters are drained off and replaced by antifreeze. Then 5 liters of the mixture are drained off and replaced by antifreeze, and so on. This process is continued until six drain-offs and replacements have been made. How much antifreeze is the final mixture?

16.44 L of antifreeze

Could you please work it out for me so I can see how you got that answer.

at each drainage even we are taking out 1/4 of the current mixture and replacing it with 5 L of pure antifreeze, leaving 3/4 of the previous mixture

after 1st drainage:
amount of antifreeze =5 L
after 2nd drainage:
amount of antifreeze = (3/4)(5) + 5 = 8.75 L
after 3rd drainage:
amount of antifreeze = (3/4)(8.75) + 5 = 11.5625 L
after 4th drainage:
amount of antifreeze = (3/5)(11.5625) + 5 = 13.671875 L
after 5th drainage:
amount of antifreeze = (3/4)(13.6718.. = 15.2539..
after 6th drainage = (3/4(15.2539..)+5 = appr 16.44 L

To solve this problem, we need to understand the concept of mixture and how it changes with each drain-off and replacement.

Let's break down the process step by step:

1. Initially, the radiator contains 20 liters of water. Since there is no antifreeze, the mixture is 100% water.

2. In the first drain-off, 5 liters of the mixture are removed. Since only water is drained off, the mixture still consists of 100% water.

3. Next, 5 liters of antifreeze are added to the radiator. This means that 5 liters of the original 20 liters are replaced by antifreeze, resulting in a mixture of 20 - 5 = 15 liters of water and 5 liters of antifreeze.

4. In the second drain-off, 5 liters of the current mixture (15 liters of water and 5 liters of antifreeze) are removed. This time, the mixture consists of both water and antifreeze.

5. Again, 5 liters of antifreeze are added to the radiator, replacing some of the drained-off mixture.

6. This process of draining off 5 liters of the current mixture and replacing it with 5 liters of antifreeze is repeated six times, as stated in the problem.

Now, let's calculate the final amount of antifreeze in the radiator:

Since there are six drain-offs and replacements, the final mixture will have 6 * 5 = 30 liters of antifreeze added.

Each drain-off and replacement step replaces 5 liters of the mixture, so the total amount of mixture drained off is 6 * 5 = 30 liters.

Since the radiator originally contained 20 liters of water, and 30 liters of mixture were drained off, there will be no water left in the radiator.

Therefore, the final mixture will consist of 30 liters of antifreeze, as all the water has been replaced.

In conclusion, the final mixture will contain 30 liters of antifreeze.