SOLUTION: A laboratory technician needs to make a 135-liter batch of a 20% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with anothe

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Question 935906: A laboratory technician needs to make a 135-liter batch of a 20% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10% to get the desired concentration?
The laboratory technician can combine --L of the pure acid solution with --L of the 10% acid solution 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+=+27+
(2) +10a+%2B+b+=+270+
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Subtract (1) from (2)
(2) +10a+%2B+b+=+270+
(1) +-a+-+b+=+-135+
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+9a+=+135+
+a+=+15+
and
(1) +a+%2B+b+=+135+
(1) +15+%2B+b+=+135+
(1) +b+=+120+
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15 liters of pure acid are needed
120 liters of 10% solution are needed
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check:
(2) +%28+a+%2B.1b+%29+%2F+135+=+.2+
(2) +%28+15+%2B.1%2A120+%29+%2F+135+=+.2+
(2) +27%2F135+=+.2+
(2) +27+=+27+
OK