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The problem in the image asks to determine how many pounds of cashews should be mixed with 10 pounds of peanuts to ensure no change in the revenue, assuming the final mixture sells for $3.50 per pound.

### Step-by-Step Solution:

1. **Peanuts cost:**
   - The store sells peanuts for **$1.50 per pound**.
   - There are **10 pounds of peanuts**, so the total revenue from the peanuts would be:
   \[
   10 \times 1.50 = 15 \, \text{dollars}
   \]

2. **Cashews cost:**
   - The store sells cashews for **$4.00 per pound**.
   - Let $ x $ be the number of pounds of cashews to be mixed with the peanuts.

3. **Mixture price:**
   - The final mixture sells for **$3.50 per pound**.
   - The total weight of the mixture will be $ 10 + x $ pounds.
   - The total revenue from the mixture should also be the same, i.e., equal to the revenue generated if the ingredients were sold separately.

4. **Set up the equation:**
   The revenue from the mixture should be the same as the revenue from selling the mixture at $3.50 per pound:
   \[
   3.50 \times (10 + x) = 1.50 \times 10 + 4.00 \times x
   \]
   Simplifying:
   \[
   35 + 3.50x = 15 + 4x
   \]
   Subtract $ 3.50x $ from both sides:
   \[
   35 = 15 + 0.50x
   \]
   Subtract 15 from both sides:
   \[
   20 = 0.50x
   \]
   Solve for $ x $:
   \[
   x = \frac{20}{0.50} = 40
   \]

### Final Answer:
The manager should mix **40 pounds of cashews** with the peanuts.

Would you like further details or have any questions?

Here are 5 questions to expand on this:

1. What would the equation look like if the mixture sold for $4.00 per pound instead of $3.50?
2. How would the problem change if there were 15 pounds of peanuts instead of 10?
3. Can you derive the total cost of the cashews mixed with peanuts?
4. What if the price of peanuts changes to $2.00 per pound? How would that affect the mixture ratio?
5. Can we solve this problem using a graphing method?

**Tip:** When mixing goods of different prices, you can always set up a weighted average formula to find the correct proportions.

A nut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per pound. But at the end of the month the peanuts had not sold well, so, in order to sell 10 pounds of peanuts, the manager decided to mix the 10 pounds of peanuts with some cashews and sell the mixture for $3.50 per pound. How many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue?

Solve a linear equation problem where a store mixes cashews and peanuts to maintain the same revenue. Learn how to calculate the pounds of cashews needed to mix with 10 pounds of peanuts sold at $1.50 per pound to match the price of $3.50 per pound for the final mixture. Suitable for students in Grades 7-9.

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