Question 1054049
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.