Alcohol mixture word problem

Question

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

Answer 1

Here's what we know:

a + 20 = s (pure alcohol plus another 20 gallons will give us a total number of solution gallons)

a + 20 * .15 = .25s (pure alcohol gal added to the 15% solution will make the solution 25%)

 

we have a value for our equation:

a + 20 * .15 = .25(a + 20)

simplify:

a + 3 = .25a + 5

Subtract .25a and 3 from both sides:

.75a = 2

Divide by .75:

a = 2 ²/₃ gallons needed

 

2 ²/₃ + 20 = s

2 ²/₃ + 20 = 22 2/₃

 

check:

2 ²/₃ + 3 = .25 * 22 ²/₃

5 ²/₃ =  5 ²/₃