SOLUTION: a tank holds 80 liters of a 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 s

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Question 783163: a tank holds 80 liters of a 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+ = liters to be drained
+.3x+ = liters of chemical in +x+ liters of solution
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+x+ liters of 30% solution are replaced with +x+
liters of 70% solution
+.7x+ = liters of chemical in 70% solution
Note that total liters of solution doesn't change
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+.3%2A80+=+24+ liters of chemical in +80+ liters of solution
+%28+24+-+.3x+%2B+.7x+%29+%2F+80+=+.4+
+%28+24+%2B+.4x+%29+%2F+80+=+.4+
+24+%2B+.4x+=+32+
+.4x+=+8+
+x+=+20+
20 liters should be drained & replaced with 70% solution
check:
+%28+24+-+.3x+%2B+.7x+%29+%2F+80+=+.4+
+%28+24+-+.3%2A20+%2B+.7%2A20+%29+%2F+80+=+.4+
+%28+24+-+6+%2B+14+%29+%2F+80+=+.4+
+32%2F80+=+.4+
+32+=+32+
OK