SOLUTION: How many gallons of a 20% solution should be mixed with 15 gallons of a 70% solution to yield a final mixture of lemonade containing 35% of pure lemon juice?

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Question 1010743: How many gallons of a 20% solution should be mixed with 15 gallons of a 70% solution to yield a final mixture of lemonade containing 35% of pure lemon juice?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = gallons of 20% solution needed
+.2x+ = gallons of pure lemon juice in 20% solution
+.7%2A15+=+10.5+ gallons of pure lemon juice in 70% solution
------------------------
+%28+.2x+%2B+10.5+%29+%2F+%28+x+%2B+15+%29+=+.35+
+.2x+%2B+10.5+=+.35%2A%28+x+%2B+15+%29+
+.2x+%2B+10.5+=+.35x+%2B+5.25+
+.15x+=+5.25+
+x+=+35+
35 gallons of 20% solution are needed
check:
+%28+.2x+%2B+10.5+%29+%2F+%28+x+%2B+15+%29+=+.35+
+%28+.2%2A35+%2B+10.5+%29+%2F+%28+35+%2B+15+%29+=+.35+
+%28+7+%2B+10.5+%29+%2F+50+=+.35+
+17.5+=+.35%2A50+
+17.5+=+17.5+
OK