To prepare 24 ounces of a 10% hydrochloric acid solution, Doreen Schmidt needs to mix 24 * 10/100 = <<24*10/100=2.4>>2.4 ounces of hydrochloric acid with 24 - 2.4 = <<24-2.4=21.6>>21.6 ounces of water.
Let's say Doreen has 24 ounces of a 12% hydrochloric acid solution and wants to know how much of a 16% solution she needs to add to it to get the desired 10% solution.
The amount of hydrochloric acid in the 12% solution is 24 * 12/100 = <<24*12/100=2.88>>2.88 ounces.
To get the desired 10% solution, Doreen needs to add an additional 2.4 - 2.88 = -0.48 ounces of hydrochloric acid. Since she cannot add a negative amount, she needs to add hydrochloric acid from a 16% solution to the 12% solution.
To add 0.48 ounces of hydrochloric acid to the solution, Doreen needs to mix 0.48 / (16/100) = 0.3 ounces of a 16% hydrochloric acid solution with the 12% solution.
Therefore, Doreen needs to mix 24 ounces of a 12% hydrochloric acid solution with 0.3 ounces of a 16% solution to get the desired 10% solution.