Question

В одном стакане было налито 150 мл молока, а в другом стакане было налито 200 мл кофе, перемешанного со 100 мл молока. Каким стало содержание кофе (в процентах) во втором стакане после того, как из второго стакана перелили 150 мл смеси в первый стакан и перемешали, а затем такой же объем полученного напитка перелили обратно из первого стакана во второй?

Answer 1

После того, как из 2-ого стакана перелили 150 мл (половину из 300мл) кофе с молоком в 1-ый стакан, во 2-ом стакане осталось:
200/2 = 100 мл кофе и 100/2 = 50 мл молока,
тогда в 1-ом стакане стало:
0 + 200/2 = 100 мл кофе и 150 + 100/2 = 200 мл молока.
После того, как из 1-ого стакана перелили во 2-ой 150 мл полученного напитка - половину его (после первого переливания получилось 300 мл напитка), то во 2-ом стакане стало:
100 + 100/2 = 150 мл кофе и 50 + 200/2 = 150 мл молока.
Получается, что кофе и молока во 2ом стакане стало поровну. Значит содержание кофе - 50%.
Ответ: 50%

Answer 2

Calculation of Coffee Content in the Second Glass

To calculate the coffee content in the second glass after transferring a portion of the mixture back and forth, we need to follow these steps:

1. Calculate the initial coffee content in the second glass. 2. Calculate the coffee content in the portion transferred to the first glass. 3. Calculate the remaining coffee content in the second glass after the transfer. 4. Calculate the final coffee content in the second glass after transferring the same volume of the mixture back.

Let's go through each step in detail.

Step 1: Calculate the Initial Coffee Content in the Second Glass

In the second glass, there were initially 200 ml of coffee mixed with 100 ml of milk. Therefore, the total volume of the mixture in the second glass is 300 ml.

To calculate the coffee content in the second glass, we need to subtract the milk content from the total volume of the mixture.

The milk content in the second glass is 100 ml, so the coffee content in the second glass is 300 ml - 100 ml = 200 ml.

Step 2: Calculate the Coffee Content in the Transferred Portion

When 150 ml of the mixture is transferred from the second glass to the first glass, the coffee and milk content in the transferred portion will be proportional to the original mixture.

Since the original mixture in the second glass had a coffee content of 200 ml and a total volume of 300 ml, we can calculate the coffee content in the transferred portion using the following proportion:

Coffee content in the transferred portion = (Coffee content in the second glass / Total volume of the mixture in the second glass) * Volume of the transferred portion

Coffee content in the transferred portion = (200 ml / 300 ml) * 150 ml = 100 ml

Therefore, the transferred portion contains 100 ml of coffee.

Step 3: Calculate the Remaining Coffee Content in the Second Glass

After transferring 150 ml of the mixture to the first glass, the remaining volume in the second glass is 300 ml - 150 ml = 150 ml.

To calculate the remaining coffee content in the second glass, we need to subtract the coffee content in the transferred portion from the initial coffee content in the second glass.

Remaining coffee content in the second glass = Initial coffee content in the second glass - Coffee content in the transferred portion

Remaining coffee content in the second glass = 200 ml - 100 ml = 100 ml

Therefore, there is 100 ml of coffee remaining in the second glass.

Step 4: Calculate the Final Coffee Content in the Second Glass after Transferring Back

When the same volume of the mixture is transferred back from the first glass to the second glass, the coffee and milk content in the transferred portion will be proportional to the remaining mixture in the first glass.

Since the remaining coffee content in the second glass is 100 ml and the remaining volume in the first glass is 150 ml, we can calculate the coffee content in the transferred portion using the following proportion:

Coffee content in the transferred portion = (Remaining coffee content in the second glass / Remaining volume in the first glass) * Volume of the transferred portion

Coffee content in the transferred portion = (100 ml / 150 ml) * 150 ml = 100 ml

Therefore, the transferred portion contains 100 ml of coffee.

Conclusion: Final Coffee Content in the Second Glass

After transferring the same volume of the mixture back from the first glass to the second glass, the coffee content in the second glass remains the same at 100 ml.

To calculate the coffee content as a percentage, we can use the following formula:

Coffee content percentage = (Coffee content / Total volume of the mixture) * 100

Coffee content percentage = (100 ml / 300 ml) * 100 = 33.33%

Therefore, the coffee content in the second glass after the transfer is approximately 33.33%.

Please note that the calculations provided are based on the information given in the question and may not account for factors such as mixing efficiency or any potential loss during the transfer process.