Question

How much water should be added to 6 gallons of pure acid to obtain a 24% acid solution?

Answer 1

To find out how much water to add to 6 gallons of pure acid to achieve a 24% acid solution, we can use the concept of concentration.

Let's denote the amount of water we need to add as \( x \) (in gallons).

**Step 1: Determine the total volume of the final solution.**

The total volume of the solution after adding water would be \( 6 + x \) gallons.

**Step 2: Set up the equation based on the percentage concentration.**

We want the final solution to be 24% acid. Therefore, the amount of acid in the final solution should be 24% of the total volume:

\[
0.24(6 + x) = 6
\]

**Step 3: Solve for \( x \).**

Now, we'll solve the equation:

\[
0.24(6 + x) = 6
\]

Distributing \( 0.24 \):

\[
1.44 + 0.24x = 6
\]

Subtract \( 1.44 \) from both sides:

\[
0.24x = 6 - 1.44
\]

\[
0.24x = 4.56
\]

Now, divide by \( 0.24 \):

\[
x = \frac{4.56}{0.24}
\]

Calculating this gives:

\[
x = 19
\]

**Conclusion:**

You should add **19 gallons of water** to 6 gallons of pure acid to obtain a 24% acid solution.