SOLUTION: How many gallons of 50% antifreeze must be mixed with 80 gallons of 20% antifreeze to get a mixture that is 40% antifreeze?

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Question 147291: How many gallons of 50% antifreeze must be mixed with 80 gallons of 20% antifreeze to get a mixture that is 40% antifreeze?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= gallons of 50% antifreeze to be added
How much antifreeze is in it?
.5x gallons
How much antifreeze is in the 20% solution?
.2%2A80+=+16 gallons
What,s the total amount of solution you end up with?
x+%2B+80
In words:
(amount of antifreeze) / (total amount of solution) = % antifreeze
%28.5x+%2B+16%29+%2F+%28x+%2B+80%29+=+.4
multiply both sides by x+%2B+80
.5x+%2B+16+=+.4%2A%28x+%2B+80%29
.5x+%2B+16+=+.4x+%2B+32
.1x+=+16
x+=+160
160 gallons of the 50% antifreeze must be added
check answer:
%28.5x+%2B+16%29+%2F+%28x+%2B+80%29+=+.4
%28.5%2A160+%2B+16%29+%2F+%28160+%2B+80%29+=+.4
%2880+%2B+16%29+%2F+240+=+.4
96+%2F+240+=+.4
96+=+.4%2A240
96+=+96
OK