Mixture Application

Question

A chemist has a 40% alcohol solution. How many gallons of water and how many gallons of the 40% alcohol solution must he mix together to obtain 30 gal of a 25\% alcohol solution?

Answer 1

X+Y = 30

the alcohol concentration is:

0.4 X + 0 * y = 0.25*30

0.4 X = 7.5

4x = 75

x = 75/4 = 18.75

y = 11.25

check:

18.75 gallons of the 40% solution contains 7.5 gallons of alcohol.

The final mixture contains 7.5/30 = 75/300 = 1/4 = 25%

So yes,

x = 75/4 = 18.75 gallons of the 40% alcohol solution

y = 11.25 gallons of water