SOLUTION: How many liters of pure alcohol must be added to 25 liters of a 26% solution to obtain a 50% solution?

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Question 264027: How many liters of pure alcohol must be added to 25 liters of a 26% solution to obtain a 50% solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(liters of alcohol in final solution)/(total liters of final solution) = 50%
In 25 liters of a 26% solution, liters of alcohol =
.26%2A25+=+6.5 liters
Let x = liters of pure alcohol to be added
%28x+%2B+6.5%29%2F%2825+%2B+x%29+=+.5
x+%2B+6.5+=+.5%2A%2825+%2B+x%29
x+%2B+6.5+=+25%2F2+%2Bx%2F2
2x+%2B+13+=+25+%2B+x
x+=+12
12 liters of pure alcohol must be added
check answer:
%28x+%2B+6.5%29%2F%2825+%2B+x%29+=+.5
%2812+%2B+6.5%29%2F%2825+%2B+12%29+=+.5
18.5%2F37+=+.5
18.5+=+18.5
OK