SOLUTION: I am so lost can you help me learn how to solve this question: How many gallons of a fruit punch containing 20% alcohol should be mixed with 2 gallons of fruit punch containing 15

Question 727848: I am so lost can you help me learn how to solve this question:
How many gallons of a fruit punch containing 20% alcohol should be mixed with 2 gallons of fruit punch containing 15% alcohol to obtain a fruit punch mixture that is 18% alcohol?
Found 2 solutions by fcabanski, josgarithmetic:
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
2 gallons of fruit punch that is 15% alcohol contains .15*2 = .3 gallons of alcohol.

x gallons of fruit punch that is 20% alcohol contains .2x gallons of alcohol.

The 5 of alcohol in the new mixture is the gallons of alcohol, .2x + .3 divided by the total gallons, x+2.

That fraction, (.2x+.3)/(2+x) = .18.

Solve it for x.

.2x + .3 = .36 + .18x

.02x = .06

x = 3 gallons.

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Only 1 variable, call it c, the amount of volume in gallons of the 20% alcohol punch to add.

To clear the confusion, you want the ratio of the alcohol to the mixture to be 0.18, or 18%.
QuantityOfAlcohol/QuantityOfPunchMixture=0.18

Solve for c.
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