SOLUTION: How many gallons of a 25% alcohol solution must be mixed with 20 gallons of a 50% alcohol solution to make 30 gallons of a 40% alcohol solution?

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Question 503890: How many gallons of a 25% alcohol solution must be mixed with 20 gallons of a 50% alcohol solution to make 30 gallons of a 40% alcohol solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = gallons of 25% solution needed
given:
+.25a+ = gallons of alcohol in 25% solution
+.5%2A20+=+10+ gallons of alcohol in 50% solution
--------------
+%28+.25a+%2B+10+%29+%2F+30+=+.4+
+.25a+%2B+10+=+.4%2A30+
+.25a+=+12+-+10+
+.25a+=+2+
+a+=+8+
8 gallons of 25% solution is needed
check:
+%28+.25a+%2B+10+%29+%2F+30+=+.4+
+%28+.25%2A8+%2B+10+%29+%2F+30+=+.4+
+12%2F30+=+.4+%7D%7D%0D%0A%7B%7B%7B+12+=+12+
OK