Question 1195288: A container contains 40L of wine which is 80% alcohol by volume. How much of the mixture should be removed and replaced by an equal volume of water so that the resulting solution will be 70%?
Found 4 solutions by josgarithmetic, math_tutor2020, Alan3354, ikleyn:
Answer by josgarithmetic(39626)   (Show Source):
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
The other tutor has the correct answer of 5 liters.
Here's how to check it:
If 5 liters are poured out, then 80% of that is pure alcohol
80% of 5 = 0.80*5 = 4
So 4 liters of pure alcohol is poured out and 1 liter is water.
The 40 L of wine drops to 40-5 = 35 L after the wine is poured, but then we replace those five liters with water to get back to 35+5 = 40 L again.
The amount of pure alcohol is not replaced. We go from 0.80*40 = 32 L to 32-4 = 28 L
Then notice that 28/40 = 0.70 = 70%
Therefore, the answer has been confirmed.
Answer by Alan3354(69443)  (Show Source):
Answer by ikleyn(52860)  (Show Source):
You can put this solution on YOUR website! .
To learn on typical percentage content of alcohol in wine, see this Internet source
https://www.masterclass.com/articles/learn-about-alcohol-content-in-wine-highest-to-lowest-abv-wines#:~:text=ABV%20is%20the%20global%20standard,with%20an%20average%20of%2018%25.
ABV is the global standard of measurement for alcohol content.
The range of ABV for unfortified wine is about 5.5% to 16%, with an average of 11.6%.
Fortified wines range from 15.5% to 25% ABV, with an average of 18%.
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