SOLUTION: How much alcohol must be added to 24 gallons of a 14% solution of alcohol in order to produce a 20% solution?

Question 1054049: How much alcohol must be added to 24 gallons of a 14% solution of alcohol in order to produce a 20% solution?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have 24 gallons of a solution that is currently 14% alcohol.

you want to add pure alcohol to this solution to get a new solution that is 20% alcohol.

let x equal the amount you want to add.

your formula is 24 * .14 + x * 1 = (24 + x) * .2

simplify this formula to get 3.36 + x = 4.8 + .2 * x

subtract .2 * x from both sides of this equation and subtract 3.36 from both sides of this equation to get x - .2 * x = 4.8 - 3.36.

simplify to get .8 * x = 1.44.

divide both sides of the equation by .8 to get x = 1.8

this says that you need to add 1.8 gallons of pure alcohol to get a solution that is 20% alcohol.

the total gallons becomes 24 + 1.8 = 25.8

the total amount of alcohol becomes .14 * 24 + 1.8 = 5.16

the percent alcohol in the new solution is 5.16 / 25.8 = .2 * 100 = 20 percent.

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