SOLUTION: How many gallons of a 5% acid solution must be mixed with 3 gallons of a 65% acid solution to make a 41% solution

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Question 663969: How many gallons of a 5% acid solution must be mixed with 3 gallons of a 65% acid solution to make a 41% solution
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of 5% solution needed
+.05a+ = gallons of acid in 5% solution
+.65%2A3+=+1.95+ = gallons of acid in 65% solution
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+%28+.05a+%2B+1.95+%29+%2F++%28+a+%2B+3+%29+=+.41+
+.05a+%2B+1.95+=+.41%2A%28+a+%2B+3+%29+
+.05a+%2B+1.95+=+.41a+%2B+1.23+
+.36a+=+1.95+-+1.23+
+.36a+=+.72+
+a+=+2+
2 gallons of 5% solution is needed
check:
+%28+.05%2A2+%2B+1.95+%29+%2F++%28+a+%2B+3+%29+=+.41+
+%28+.1+%2B+1.95+%29+%2F+%28+2+%2B+3+%29+=+.41+
+2.05+=+.41%2A%28+2+%2B+3+%29+
+2.05+=+.41%2A5+
+2.05+=+2.05+
OK