SOLUTION: A doctor mixed a 10% glucose solution with a 20% glucose solution. This mixture produced 16 oz of an 18% glucose solution. How many liters of each solution did the doctor use?

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Question 617197: A doctor mixed a 10% glucose solution with a 20% glucose solution. This mixture produced 16 oz of an 18% glucose solution. How many liters of each solution did the doctor use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of 10% solution used
Let +b+ = ounces of 20% solution used
+.1a+ = ounces of glucose in 10% solution
+.2b+ = ounces of glucose in 20% solution
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given:
(1) +a+%2B+b+=+16+
(2) +%28+.1a+%2B+.2b+%29+%2F+16+=+.18+
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(2) +.1a+%2B+.2b+=+.18%2A16+
(2) +.1a+%2B+.2b+=+2.88+
(2) +10a+%2B+20b+=+288+
(2) +5a+%2B+10b+=+144+
Multiply both sides of (1) by 5
and subtract from (2)
(2) +5a+%2B+10b+=+144+
(1) +-5a+-+5b+=+-80+
+5b+=+64+
+b+=+12.8+
and
(1) +a+%2B+b+=+16+
(1) +a+%2B+12.8+=+16+
(1) +a+=+3.2+
3.2 ounces of 10% solution is used
12.8 ounces of 20% solution is used
check:
(2) +%28+.1%2A3.2+%2B+.2%2A12.8+%29+%2F+16+=+.18+
(2) +.32+%2B+2.56+=+.18%2A16+
(2) +2.88+=+2.88+
OK