\textbf{Step 1: Define What We Know}
- Let x be the ounces of the 10% brass alloy added.
- The amount of brass in the 10% alloy is 0.10x.
- The amount of brass in the 70% alloy is 0.70 \times 2,585.
- Total weight of the final mixture is x + 2,585 ounces.
- The total amount of brass in the final mixture is 0.10x + 0.70 \times 2,585.
\textbf{Step 2: Set Up the Equation}
The equation for the final concentration of brass in the mixture:
\frac{0.10x + 0.70 \times 2,585}{x + 2,585} = 0.65
\textbf{Step 3: Solve the Equation}
Expanding and simplifying the equation:
0.10x + 0.70 \times 2,585 = 0.65x + 0.65 \times 2,585
0.70 \times 2,585 - 0.65 \times 2,585 = 0.65x - 0.10x
Solving, we get x = 235.0
\textbf{Answer:} \ x = 235.0 \text{ ounces}