SOLUTION: A 50 gallon of mixture contains 20% alcohol and 80%orange juice,how much pure alcohol should be added to this mixture to make it 50% alcohol content?

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Question 760829: A 50 gallon of mixture contains 20% alcohol and 80%orange juice,how much pure alcohol should be added to this mixture to make it 50% alcohol content?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = gallons of pure alcohol to be added
+.2%2A50+=+10+ = gallons of pure alcohol in 20% mixture
------------------
+%28+10+%2B+x+%29+%2F+%28+50+%2B+x+%29+=+.5+
+10+%2B+x+=+.5%2A%28+50+%2B+x+%29+
+10+%2B+x+=+25+%2B+.5x+
+.5x+=+15+
+x+=+30+
30 gallons of pure alcohol needs to be added
check:
+%28+10+%2B+x+%29+%2F+%28+50+%2B+x+%29+=+.5+
+%28+10+%2B+30+%29+%2F+%28+50+%2B+30+%29+=+.5+
+40%2F80+=+.5+
+40+=+.5%2A80+
+40+=+40+
OK