# solve this word problem

label Algebra
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how many quarts of water should be mixed with a 30% vinegar solution to obtain a 12 quart of a 25% vinegar solution?

Oct 3rd, 2015

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.

As follows:

x=quarts of 30% vinegar solution

y=quarts of water

(1) x+y=12

AND

(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

.3x=3

x=3/.3

x=10

Then plug into the first equation

10+y=12

y=2

Sep 18th, 2015

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Oct 3rd, 2015
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Oct 3rd, 2015
Nov 18th, 2017
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