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This problem can be solved using a weighted average approach, where we determine how many pounds of cashews need to be mixed with peanuts to achieve the desired cost per pound of the mixed nuts.

Let:
- $ x $ = the number of pounds of cashews to be mixed.
- The price per pound of cashews is $14.
- The price per pound of peanuts is $6.50, and there are 5 pounds of peanuts.
- The target price for the mixed nuts is $10.25 per pound.

We can set up the following equation based on the total cost of the mixed nuts:

\[
14x + 6.50(5) = 10.25(x + 5)
\]

Now, let's solve this step by step:

1. Simplify both sides:

\[
14x + 32.50 = 10.25(x + 5)
\]
\[
14x + 32.50 = 10.25x + 51.25
\]

2. Subtract $ 10.25x $ from both sides:

\[
14x - 10.25x + 32.50 = 51.25
\]
\[
3.75x + 32.50 = 51.25
\]

3. Subtract 32.50 from both sides:

\[
3.75x = 18.75
\]

4. Solve for $ x $:

\[
x = \frac{18.75}{3.75} = 5
\]

Thus, **5 pounds of cashews** need to be mixed with 5 pounds of peanuts to achieve the desired price of $10.25 per pound.

Would you like any further details on this solution or have any other questions?

Here are 5 related questions you might find helpful:
1. How would the equation change if the price of peanuts was $7 per pound instead of $6.50?
2. What if the target price for the mixed nuts was $9 per pound?
3. How would you approach the problem if there were 10 pounds of peanuts instead of 5?
4. What is the total cost of the mixed nuts when the correct ratio is used?
5. How does the weight of peanuts affect the ratio of cashews needed?

**Tip:** In mixture problems, always set up the equation based on the total cost to find the correct balance between the different components.

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 solve a weighted average problem where you mix cashews costing $14 per pound with 5 pounds of peanuts costing $6.50 per pound to create mixed nuts costing $10.25 per pound. This detailed solution is suitable for students in Grades 9-12.

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