How much pure acid must be added to 12 ounces of a 40% acid solution to achieve a 60% solution?

To determine how much pure acid needs to be added to a solution in order to achieve a desired concentration, we should first calculate the amount of acid currently present in the initial solution and then find out how much pure acid needs to be added to reach the target concentration.

In this scenario, we start with 12 ounces of a 40% acid solution. To find the amount of pure acid in this solution, we multiply the total volume by the percentage of acid:

12 ounces * 0.40 = 4.8 ounces of pure acid.

Let the amount of pure acid we need to add be denoted by x ounces. After adding x ounces of pure acid, the total amount of acid in the solution will become:

4.8 ounces + x ounces.

The total volume of the solution after adding x ounces will be:

12 ounces + x ounces.

We want the final solution to be 60% acid. Therefore, we can set up the equation that represents this concentration:

(4.8 + x) / (12 + x) = 0.60.

To eliminate the fraction, we can cross-multiply:

4.8 + x = 0.60 * (12 + x).

Expanding the right side gives