SOLUTION: how much 40% alcohol solution and 25% solution must be mixed together to get 24 gallons of 30% solution?

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Question 356464: how much 40% alcohol solution and 25% solution must be mixed together to get 24 gallons of 30% solution?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Let A be the amount of 40% solution, B the amount of 25% solution.
Volume:
1.A%2BB=24
Concentration:
40A%2B25B=30%2824%29
2.8A%2B5B=144
Multiply eq. 1 by (-5) and add to eq. 2 to eliminate B and solve for A.
-5A-5B%2B8A%2B5B=-120%2B144
3A=24
highlight%28A=8%29gallons
Then from eq. 1,
8%2BB=24
highlight%28B=16%29gallons