SOLUTION: a laboratory needs to make 135 litter batch of a 20% acid solution. How can the laboratory combine a batch of acid solution the is pure acid with another that is 10%to get the des

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Question 713127: a laboratory needs to make 135 litter batch of a 20% acid solution. How can the laboratory combine a batch of acid solution the is pure acid with another that is 10%to get the desired concentration
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of pure acid needed
Let +b+ = liters of 10% solution needed
+.1b+ = liters of pure acid in 10% solution
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(1) +a+%2B+b+=135+
(2) +%28+a+%2B+.1b+%29+%2F+135+=+.2+
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(2) +a+%2B+.1b+=+.2%2A135+
(2) +a+%2B+.1b+=+27+
(2) +10a+%2B+b+=+270+
Subtract (1) from (2)
(2) +10a+%2B+b+=+270+
(1) +-a+-+b+=+-135+
+9a+=+135+
+a+=+15+
and, since
(1) +a+%2B+b+=135+
(1) +15+%2B+b+=135+
(1) +b+=+135+-+15+
(1) +b+=+120+
15 liters of pure acid are needed
120 liters of 10% solution are needed
check:
(2) +%28+a+%2B+.1b+%29+%2F+135+=+.2+
(2) +%28+15+%2B+.1%2A120+%29+%2F+135+=+.2+
(2) +%28+15+%2B+12+%29+%2F+135+=+.2+
(2) +27+=+.2%2A135+
(2) +27+=+27+
OK