Certainly! Let's solve this step-by-step:
### Given:
- We have 18 liters of a bleach solution with a concentration of 14%.
- We need to find out how many liters of water should be added so that the resulting solution has a concentration of 10%.
### Step-by-Step Solution:
1. Calculate the amount of bleach in the original solution:
- The concentration of bleach is 14%, which corresponds to [tex]\(0.14\)[/tex] as a decimal.
- The original volume of the solution is 18 liters.
- Therefore, the amount of bleach in the original solution is:
[tex]\[
\text{Amount of bleach} = 0.14 \times 18 = 2.52 \text{ liters}
\][/tex]
2. Set up the equation for the final solution:
- Let [tex]\( x \)[/tex] be the volume of water to be added.
- After adding [tex]\( x \)[/tex] liters of water, the total volume of the solution becomes [tex]\( 18 + x \)[/tex] liters.
- The concentration of bleach in the final solution should be 10%, which corresponds to [tex]\(0.10\)[/tex] as a decimal.
3. Establish the concentration relationship:
- The amount of bleach remains the same in both the original and the final solutions, which is [tex]\(2.52\)[/tex] liters.
- The final concentration of the bleach in the new solution is given by:
[tex]\[
\frac{\text{Amount of bleach}}{\text{Total volume}} = \text{Final concentration}
\][/tex]
- Plugging in the known values:
[tex]\[
\frac{2.52}{18 + x} = 0.10
\][/tex]
4. Solve the equation for [tex]\( x \)[/tex]:
- Multiply both sides of the equation by [tex]\((18 + x)\)[/tex]:
[tex]\[
2.52 = 0.10 \times (18 + x)
\][/tex]
- Simplify and isolate [tex]\( x \)[/tex]:
[tex]\[
2.52 = 1.8 + 0.10x
\][/tex]
[tex]\[
2.52 - 1.8 = 0.10x
\][/tex]
[tex]\[
0.72 = 0.10x
\][/tex]
[tex]\[
x = \frac{0.72}{0.10} = 7.2
\][/tex]
### Conclusion:
To reduce the concentration of the bleach solution from 14% to 10%, you need to add 7.2 liters of water.
Among the given options, the correct answer is:
7.2 liters
