SOLUTION: How many liters of 80% alcohol solution and 20% alcohol solution must be mixed to obtain 3 liters of 60% alcohol solution?

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Question 1051506: How many liters of 80% alcohol solution and 20% alcohol solution must be mixed to obtain 3 liters of 60% alcohol solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 80% alcohol solution needed
Let +b+ = liters of 20% alcohol solution needed
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(1) +a+%2B+b+=+3+
(2) +%28+.8a+%2B+.2b+%29+%2F+3+=+.6+
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(2) +.8a+%2B+.2b+=+1.8+
(2) +8a+%2B+2b+=+18+
(2) +4a+%2B+b+=+9+
-----------------------
subtract (1) from (2)
(2) +4a+%2B+b+=+9+
(1) +-a+-+b+=+-3+
--------------------
+3a+=+6+
+a+=+2+
and
(1) +2+%2B+b+=+3+
(1) +b+=+1+
2 liters of 80% alcohol solution are needed
1 liter of 20% alcohol solution is needed
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check:
(2) +%28+.8a+%2B+.2b+%29+%2F+3+=+.6+
(2) +%28+.8%2A2+%2B+.2%2A1+%29+%2F+3+=+.6+
(2) +%28+1.6+%2B+.2+%29+%2F+3+=+.6+
(2) +1.8+=+3%2A.6+
(2) +1.8+=+1.8+
OK