SOLUTION: James has avalible a 10% alcohal solution and a 60% solution. Find how many liters of each solution should be mixed to make 50 liters of 40% solution.

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Question 490730: James has avalible a 10% alcohal solution and a 60% solution. Find how many liters of each solution should be mixed to make 50 liters of 40% solution.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = liters of 10% solution needed
Let b = liters of 60% solution needed
given:
(1) +a+%2B+b+=+50+
(2) +%28+.1a+%2B+.6b%29+%2F+50+=+.4+
------------------------
(2) +.1a+%2B+.6b+=+20+
(2) +a+%2B+6b+=+200+
Subtract (1) from (2)
(2) +a+%2B+6b+=+200+
(1) +-a+-+b+=+-50+
+5b+=+150+
+b+=+30+
and, since
(1) +a+%2B+b+=+50+
(1) +a+%2B+30+=+50+
(1) +a+=+20+
20 liters of 10% solution and 30
liters of 60% solution are needed
check:
(2) +%28+.1a+%2B+.6b%29+%2F+50+=+.4+
(2) +%28+.1%2A20+%2B+.6%2A30%29+%2F+50+=+.4+
(2) +%28+2+%2B+18%29+%2F+50+=+.4+
(2) +20%2F50+=+.4+
(2) +20+=+20+
OK