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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.

How many pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixed nuts that cost $10.25 per pound?

Learn how to calculate the pounds of cashews needed to mix with peanuts to create a nut mixture costing $10.25 per pound. This problem involves using weighted averages and solving linear equations. Suitable for students in Grades 8-10.

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