Question
I need you to give me the result of the following exercise There are two two-liter bottles, one with a liter of wine and the other with a liter of water. Transfer 1/2 of the contents of the water bottle to the wine bottle and mix thoroughly. The mixture from the wine bottle is then returned to the water bottle, so that the two bottles again have 1 liter of liquid each. In which of the two bottles was more water left? How much wine was left in the water bottle?
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Answer to a math question I need you to give me the result of the following exercise There are two two-liter bottles, one with a liter of wine and the other with a liter of water. Transfer 1/2 of the contents of the water bottle to the wine bottle and mix thoroughly. The mixture from the wine bottle is then returned to the water bottle, so that the two bottles again have 1 liter of liquid each. In which of the two bottles was more water left? How much wine was left in the water bottle?
Nash
4.987 Answers
This is a classic problem of liquid transfer between two containers. Initially, we have 1 liter of wine in one bottle and 1 liter of water in the other bottle.
Step 1: Transfer 1/2 liter of water to the wine bottle.
Wine bottle: 1 liter of wine + 0.5 liters of water
Water bottle: 0.5 liters of water
Step 2: Mix thoroughly.
The wine bottle now contains a mixture that is 1/3 water and 2/3 wine.
Step 3: Transfer 1/2 liter of the mixture back to the water bottle.
Water transferred in: 1/3 * 0.5 = 1/6 liters
Wine transferred in: 2/3 * 0.5 = 1/3 liters
Final contents in the wine bottle:
- Wine: 2/3 liters
- Water: 1/3 liters
Final contents in the water bottle:
- Water: 0.5 + 1/6 = 2/3 liters
- Wine: 1/3 liters
More water is left in the: water bottle (2/3 liters)
Amount of wine left in the: water bottle (1/3 liters)
Therefore, both bottles end up with equal amounts of 'foreign' liquid.
{Answer:} The water bottle has more water left, 2/3 liters of water, and there is 1/3 liters of wine in the water bottle.
Step 1: Transfer 1/2 liter of water to the wine bottle.
Wine bottle: 1 liter of wine + 0.5 liters of water
Water bottle: 0.5 liters of water
Step 2: Mix thoroughly.
The wine bottle now contains a mixture that is 1/3 water and 2/3 wine.
Step 3: Transfer 1/2 liter of the mixture back to the water bottle.
Water transferred in: 1/3 * 0.5 = 1/6 liters
Wine transferred in: 2/3 * 0.5 = 1/3 liters
Final contents in the wine bottle:
- Wine: 2/3 liters
- Water: 1/3 liters
Final contents in the water bottle:
- Water: 0.5 + 1/6 = 2/3 liters
- Wine: 1/3 liters
More water is left in the: water bottle (2/3 liters)
Amount of wine left in the: water bottle (1/3 liters)
Therefore, both bottles end up with equal amounts of 'foreign' liquid.
{Answer:} The water bottle has more water left, 2/3 liters of water, and there is 1/3 liters of wine in the water bottle.
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