How much pure alcohol should I add?

Question

How many gallons of pure alcohol should be mixed with 20 gal of a 15% alcohol solution to get a mixture that is 25% alcohol?

Answer 1

Let x = number of gallons of 100% alcohol solution

    

20 = number of gallons of 15% alcohol solution

 

x+20 = number of gallons of 25% alcohol solution

 

The amount of alcohol in a solution is found by multiplying the number of gallons of solution by the percentage (as a decimal) of alcohol that the solution contains.  

 

Alcohol content of 100% solution = 1.00x = x

Alcohol content of 15% solution = 0.15(20) = 3

Alcohol content of mixture (25% solution) = 0.25(x+20) = 0.25x + 5

 

So, x + 3 = 0.25x + 5

 

        0.75x = 2

 

              x = 2 2/3 gallons