SOLUTION: How many gallons of pure alcohol must be mixed with 5 gallons of a solution that is 20 percent to make a solution that is 50% alcohol?

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Question 631697: How many gallons of pure alcohol must be mixed with 5 gallons of a solution that is 20 percent to make a solution that is 50% alcohol?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of pure alcohol needed
+.2%2A5+=+1+ gallons of pure alcohol in 20% solution
given:
+%28+a+%2B+1+%29+%2F+%28+a+%2B+5+%29+=+.5+
+a+%2B+1+=+.5%2A%28+a+%2B+5+%29+
+a+%2B+1+=+.5a+%2B+2.5+
+a+-+.5a+=+2.5+-+1+
+.5a+=+1.5+
+a+=+3+
3 gallons of pure alcohol are needed
check:
+%28+a+%2B+1+%29+%2F+%28+a+%2B+5+%29+=+.5+
+%28+3+%2B+1+%29+%2F+%28+3+%2B+5+%29+=+.5+
+4%2F8+=+.5+
+.5+=+.5+
OK