SOLUTION: Suppose that you have a supply of a 40% solution of alcohol and a 60% solution of alcohol. How many quarts of each should be mixed to produce 90 quarts that is 50% alcohol?

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Question 658959: Suppose that you have a supply of a 40% solution of alcohol and a 60% solution of alcohol. How many quarts of each should be mixed to produce 90 quarts that is 50% alcohol?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = quarts of 40% solution needed
Let b = quarts of 60% solution needed
given:
(1) +a+%2B+b+=+90+
(2) +%28+.4a+%2B+.6b+%29+%2F+90+=+.5+
--------------------------
(2) +.4a+%2B+.6b+=+.5%2A90+
(2) +.4a+%2B+.6b+=+45+
(2) +4a+%2B+6b+=+450+
--------------------
Multiply both sides of (1) by +4+
and subtract (1) from (2)
(2) +4a+%2B+6b+=+450+
(1) +-4a+-+4b+=+-360+
+2b+=+90+
+b+=+45+
and, since
(1) +a+%2B+b+=+90+
(1) +a+%2B+45+=+90+
(1) +a+=+45+
45 quarts of 40% solution are needed
45 quarts of 60% solution are needed
check:
(2) +%28+.4%2A45+%2B+.6%2A45+%29+%2F+90+=+.5+
(2) +%28+18+%2B+27+%29+%2F+90+=+.5+
(2) +45+%2F+90+=+.5+
(2) +45+=+.5%2A90+
(2) +45+=+45+
OK