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You want to obtain 12 quarts of a 25% vinegar solution using a 30% vinegar solution and water.
You need to dilute the 30% solution to 25%, which means diluting it by 20% (30/25=1.2).
So you would mix 10 quarts of the 30% vinegar solution, and 2 quarts of pure water (20% of 10) to achieve a 25% vinegar solution.
You can also solve algebraically by setting up two equations. This is the standard way to solve problems like this, especially when they are more complicated.
x=quarts of 30% vinegar solution
y=quarts of water
(2) .3x + 0y = .25(12)
(you multiply x by .3 because it is a 30% solution, you multiply y by 0 because it is a 0% solution, and you multiply 12 by .25 because you want 12 liters of a 25% solution.)
Solve the second equation
Then plug into the first equation
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