A store sells cashews for $ 5.00 per pound and peanuts for $ 1.50 per pound.  The manager decides to mix 60 pounds of peanuts with some cashews and sell the mixture for $ 3.00 per pound.  How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts​ separately?
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Part 1
There should be 
  
enter your response here pounds of cashews in the mixture.

To solve this problem, we need to find the number of pounds of cashews, $ x $, that should be mixed with 60 pounds of peanuts to create a mixture that can be sold for $3.00 per pound and generate the same revenue as selling the peanuts and cashews separately.

### Step-by-step solution:

1. **Revenue from selling nuts separately:**
   - Revenue from selling 60 pounds of peanuts at $1.50 per pound:  
   \[
   \text{Revenue from peanuts} = 60 \times 1.50 = 90 \text{ dollars}
   \]
   - Revenue from selling $ x $ pounds of cashews at $5.00 per pound:  
   \[
   \text{Revenue from cashews} = x \times 5.00 = 5x \text{ dollars}
   \]
   - Total revenue from selling the nuts separately:  
   \[
   \text{Total separate revenue} = 90 + 5x
   \]

2. **Revenue from selling the mixture:**
   The total weight of the mixture is $ 60 + x $ pounds, and the price is $3.00 per pound.  
   Revenue from selling the mixture:
   \[
   \text{Revenue from mixture} = (60 + x) \times 3 = 180 + 3x
   \]

3. **Setting up the equation:**
   To find $ x $, set the revenue from the mixture equal to the revenue from selling the nuts separately:
   \[
   180 + 3x = 90 + 5x
   \]

4. **Solve for $ x $:**
   \[
   180 - 90 = 5x - 3x
   \]
   \[
   90 = 2x
   \]
   \[
   x = 45
   \]

### Final Answer:
There should be **45 pounds of cashews** in the mixture.

Would you like more details or have any questions?

Here are 5 related questions to expand this concept:
1. What is the total weight of the final mixture?
2. How would the solution change if the price of peanuts increased to $2.00 per pound?
3. What would happen to the mixture price if the manager wanted to make a higher profit margin?
4. How can you calculate the percentage of cashews in the final mixture?
5. How would you solve this problem if the price per pound of the mixture was $4.00 instead of $3.00?

**Tip:** When mixing two products with different prices, the overall price per pound can be found by balancing the ratio of their quantities and costs.

A store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. The manager decides to mix 60 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?

Find out how many pounds of cashews should be mixed with 60 pounds of peanuts to match revenue when the mixture is sold for $3.00 per pound. This problem covers algebra, linear equations, and revenue calculation, suitable for students in Grades 9-11.

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