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How much pure acid must be added to 10 ounces of a 50% acid solution to obtain a 75% acid solution?

5 ounces

6 ounces

10 ounces

To determine how much pure acid needs to be added to a 10-ounce solution of 50% acid in order to obtain a 75% acid solution, we start by calculating the current amount of pure acid in the solution.

A 50% acid solution means that in 10 ounces, there are 5 ounces of pure acid (50% of 10 ounces). When pure acid is added, the total volume of the solution increases, and we want the final concentration to be 75%.

Let’s denote the amount of pure acid added as \( x \) ounces. After adding \( x \) ounces of pure acid, the new total volume of the solution will be \( 10 + x \) ounces, and the total amount of pure acid will be \( 5 + x \) ounces.

To achieve a 75% concentration, the equation can be set up as follows:

\[

\frac{5 + x}{10 + x} = 0.75

\]

Next, we solve for \( x \):

1. Cross-multiply to eliminate the fraction:

\[

5 + x = 0.75(10 + x)

\]

2. Distribute the 0.75:

\

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8 ounces

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