SOLUTION: How many gallons each of 25% alcohol and 35% alcohol should be mixed to get 20 gallons of 32% alcohol?

Question 129615: How many gallons each of 25% alcohol and 35% alcohol should be mixed to get 20 gallons of 32% alcohol?
Answer by kev82(151) (Show Source): You can put this solution on YOUR website!
If we take X gallons of the 25% liquid, and Y gallons of the 35% liquid, then it is quite obvious that we will have X+Y gallons of liquid in total. We need to make 20 gallons of liquid so X+Y=20.
Let us now consider the amount of alcohol in our solution. Taking X gallons of the first liquid will give us 0.25X gallons of alcohol because 25% of the liquid is alcohol. Similarly taking Y gallons of the second liquid gives us 0.35Y gallons of alcohol, so in total there are 0.25X+0.35Y gallons of alcohol in the final mixture.
The final mixture is 20 gallons as we know, so the percentage of alcohol in it is (0.25X+0.35Y)/20. This must be 0.32 (32%) This gives us the second equation (0.25X+0.35Y)/20=0.32. So we now have:
X+Y=20
0.25X+0.35Y=6.4
These equations can be solved for X and Y which should give your answer.
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