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To determine how many gallons of a 15% sodium hypochlorite solution are needed to make 115 gallons of a 9% solution, you can use the concept of dilution and the equation that relates the concentrations and volumes of the two solutions involved.

Let’s define the variables:

- C1 = concentration of the first solution (15% or 0.15)

- V1 = volume of the first solution (unknown, what we are solving for)

- C2 = concentration of the desired solution (9% or 0.09)

- V2 = volume of the desired solution (115 gallons)

According to the dilution equation, the amount of the chemical in the solution can be expressed as:

\[ C1 \times V1 = C2 \times V2 \]

Substituting the known values into the equation:

\[ 0.15 \times V1 = 0.09 \times 115 \]

Calculating the right side:

\[ 0.09 \times 115 = 10.35 \text{ gallons of active ingredient} \]

Now, substitute this value back into the equation:

\[ 0.15 \times V1 = 10.35 \]

To find V1