SOLUTION: A mixture of 10% disinfectant solution is to be made from 11% and 7% disinfectant solutions. How much of each solution should be used if 44 gallons of 10% solution are needed?

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Question 418674: A mixture of 10% disinfectant solution is to be made from 11% and 7% disinfectant solutions. How much of each solution should be used if 44 gallons of 10% solution are needed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = gallons of 11% solution needed
Let b = gallons of 7% solution needed
given:
(1) a+%2B+b+=+44
+%28+.11a+%2B+.07b+%29%2F44+=+.1+
.11a+%2B+.07b+=+4.4+
(2) 11a+%2B+7b+=+440+
------------------
Multiply both sides of (1) by 7
and subtract (1) from (2)
(2) 11a+%2B+7b+=+440+
(1) -7a+-+7b+=+-308+
4a+=+132+
+a+=+33+
and, since
+a+%2B+b+=+44+
+b+=+44+-+33+
b+=+11
33 gallons of 11% solution are needed
11 gallons of 7% solution are needed
check answer:
+%28+.11a+%2B+.07b+%29%2F44+=+.1+
+%28+.11%2A33+%2B+.07%2A11+%29%2F44+=+.1+
+%28+3.63+%2B+.77+%29+%2F+44+=+.1+
+4.4+%2F+44+=+.1+
4.4+=+4.4+
OK