SOLUTION: In a chemistry class, 12 L of a 12% alcohol solution must be mixed with a 2% solution to get a 14% solution. How many liters of the 20% solution are needed?

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Question 126568: In a chemistry class, 12 L of a 12% alcohol solution must be mixed with a 2% solution to get a 14% solution. How many liters of the 20% solution are needed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(amount of alcohol needed) / (total amount of solution) = 20%
In the 12% solution I have
12%2A.12+=+1.44liters alcohol
Let x be the amount of 20% solution needed
%281.44+%2B+.2x%29+%2F+%2812+%2B+x%29+=+.14
1.44+%2B+.2x+=+.14%2812+%2B+x%29
1.44+%2B+.2x+=+1.68+%2B+.14x
.06x+=+.24
x+=+4
4 liters of the 20% solution are needed
check
%281.44+%2B+.2x%29+%2F+%2812+%2B+x%29+=+.14
%281.44+%2B+.2%2A4%29+%2F+%2812+%2B+4%29+=+.14
%281.44+%2B+.8%29+%2F+16+=+.14
2.24+%2F+16+=+.14
.14+=+.14
OK