SOLUTION: How many gallons of 40 percent alcohol solution must be mixed with 70 percent solution to obtain 30 gallons of a 52 percent alcohol solution?

Question 278196: How many gallons of 40 percent alcohol solution must be mixed with 70 percent solution to obtain 30 gallons of a 52 percent alcohol solution?
Answer by Grinnell(63) (Show Source): You can put this solution on YOUR website!
Since you will end up with 30 gallons, let 30-x represent the number of gallons of 40% solution AND let x represent the number of gallons at 70% solution. We then have: .40(30-x)+.70x=.52(30)
Just multiply by 100 to remove that ugly old decimal to make life easier (for now), ok? Then off to the races!
1200-40x+70x=1560
30x=360
x=12
.40(18)+.70(12)=.52(30) (Yes, hello to Mr. Decimal again, to check our work!)
7.2+8.4=15.6 It checks out!
The answer is 18 gallons. Does this make sense to you? Am I clear? Let me hear from you, OK?
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