How many ounces of a 11% alcohol solution and a 31% alcohol solution must be combined to obtain 75 ounces of a 15 % solution?

Answer 1

Reece, these are just disguised mass balance equations. The total mass of alcohol before mixing must be the same as in the mixture.

Suppose we need x oz of the 11% solution and y oz of the 31% solution.

Start with the mixture: 75 ounces of a 15% solution ⇒ it contains 75 x 0.15 = 11.25 ounces of alcohol.

The two mixing solutions contain 0.11x and 0.31y oz of alcohol, respectively.

Therefore, 0.11x + 0.31y = 11.25

Or 11x + 31y = 1125 . . . . . (1)

And x + y = 75 . . . . . . . . (2)

These are 2 simple simultaneous equations which I leave for you to solve.