The problem asks to find how many pounds of cashews must be mixed with 5 pounds of peanuts to achieve a mixture that costs $10.25 per pound. The cost per pound of cashews is $14, and the cost per pound of peanuts is $6.50.

Let the unknown quantity of cashews be $x$ pounds.

We will set up a weighted average equation based on the costs:

$\frac{14x + 6.5 \times 5}{x + 5} = 10.25$

Step-by-step solution:

1. Multiply both sides by $(x + 5)$ to clear the denominator: $14x + 6.5 \times 5 = 10.25(x + 5)$

2. Simplify the equation: $14x + 32.5 = 10.25(x + 5)$ $14x + 32.5 = 10.25x + 51.25$

3. Move all terms involving $x$ to one side: $14x - 10.25x = 51.25 - 32.5$ [ 3.75x = 18.