SOLUTION: A car radiator contains 10 liters of 20% anitfreeze solution. How many liters of pure antifreeze are needed to make the solution 50% antifreeze without replacement?

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Question 219499: A car radiator contains 10 liters of 20% anitfreeze solution. How many liters of pure antifreeze are needed to make the solution 50% antifreeze without replacement?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This assumes that the radiator will hold whatever added
antifreeze you try to put in.
In words:
(final liters of antifreeze)/(final liters of total mixture) = 50%
Let a = liters of antifreeze to be added
%28.2%2A10+%2B+a%29%2F%2810+%2B+a%29+=+.5
Multiply both sides by 10+%2Ba
2+%2B+a+=+.5%2A%2810+%2B+a%29
2+%2B+a+=+5+%2B+.5a
.5a+=+5+-+2
.5a+=+3
a+=+6
6 liters of antifreeze needs to be added to make mixture 50%
check answer:
%28.2%2A10+%2B+6%29%2F%2810+%2B+6%29+=+.5
%282+%2B+6%29%2F16+=+.5
8%2F16+=+.5
.5+=+.5
OK