SOLUTION: A tank holds 80 gallons of chemical solution. Currently the solution has a strength of 30%. How much of this should be drained and replaced with a 70% solution to get a final stren

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Question 147290: A tank holds 80 gallons of chemical solution. Currently the solution has a strength of 30%. How much of this should be drained and replaced with a 70% solution to get a final strength of 40%?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= amount of 30% solution to be drained and replaced with
70% solution
Currently, how much chemical is in the 30% solution?
.3%2A80+=+24 gallons
How much chemical will be in the amount drained off?
.3x
Then how much chemical will be in the solution that is put back in?
.7x
In words:
(amount of chemical I end up with) / (amount of solution I end up with) =
final strength of solution
%2824+-+.3x+%2B+.7x%29+%2F+%2880+-+x+%2B+x%29+=+.4
%2824+%2B+.4x%29+%2F+80+=+.4
24+%2B+.4x+=+.4%2A80
24+%2B+.4x+=+32
.4x+=+8
x+=+20
20 gallons must be drained off and replaced with 70% solution
check answer:
%2824+%2B+.4x%29+%2F+80+=+.4
24+%2B+.4%2A20%29+%2F+80+=+.4
24+%2B+8%29+%2F+80+=+.4
32%2F80+=+.4
32+=+32
OK