To solve the problem of determining how many liters of water should be added to 18 liters of a 14% bleach solution so that the resulting solution contains only 10% bleach, we can follow these steps:
1. Calculate the amount of bleach in the original solution:
The original solution is 18 liters with 14% bleach.
[tex]\[
\text{Amount of bleach}_{\text{original}} = 18 \text{ liters} \times 0.14 = 2.52 \text{ liters}
\][/tex]
2. Determine the final volume of the solution after adding water:
Let [tex]\( x \)[/tex] be the amount of water to be added. The total volume of the resulting solution will be [tex]\( 18 \text{ liters} + x \text{ liters} \)[/tex].
3. Set up the equation for the final concentration of bleach:
After adding [tex]\( x \)[/tex] liters of water, the concentration of bleach will be 10%. The amount of bleach remains the same (2.52 liters), but the total volume of the solution changes.
Thus, the equation for the new concentration can be written as:
[tex]\[
\frac{\text{Amount of bleach}_{\text{original}}}{\text{Total volume of the new solution}} = 0.10
\][/tex]
Substituting the known values:
[tex]\[
\frac{2.52 \text{ liters}}{18 \text{ liters} + x} = 0.10
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we solve the equation:
[tex]\[
2.52 = 0.10 \times (18 + x)
\][/tex]
First, distribute the 0.10:
[tex]\[
2.52 = 1.8 + 0.10x
\][/tex]
Next, isolate [tex]\( x \)[/tex] by subtracting 1.8 from both sides:
[tex]\[
2.52 - 1.8 = 0.10x
\][/tex]
[tex]\[
0.72 = 0.10x
\][/tex]
Finally, solve for [tex]\( x \)[/tex] by dividing both sides by 0.10:
[tex]\[
x = \frac{0.72}{0.10} = 7.2
\][/tex]
Therefore, [tex]\( 7.2 \)[/tex] liters of water should be added to the original solution to achieve a 10% bleach concentration.
The correct answer is:
[tex]\[ \boxed{7.2 \text{ liters}} \][/tex]
