A nut wholesaler sells a mix of peanuts and cashews. He charges $2.80 per pound for peanuts and $5.30 per pound for cashews. If the mix is to sell for $4.80 per pound, how many pounds each of peanuts and cashews should be used to make 100 pounds of the mix?
peanuts    	
 lb
cashews

We can solve this problem using a system of equations. Let:

- $ x $ be the number of pounds of peanuts,
- $ y $ be the number of pounds of cashews.

We are given the following information:

1. The total weight of the mix is 100 pounds:
   \[
   x + y = 100
   \]
   
2. The price per pound of the mix is $4.80, so the total cost of the mix is:
   \[
   2.80x + 5.30y = 4.80 \times 100 = 480
   \]

We now have the following system of equations:
1. $ x + y = 100 $
2. $ 2.80x + 5.30y = 480 $

### Solving the system of equations:

From the first equation:
\[
y = 100 - x
\]

Substitute this into the second equation:
\[
2.80x + 5.30(100 - x) = 480
\]

Now expand and solve for $ x $:
\[
2.80x + 530 - 5.30x = 480
\]
\[
-2.50x + 530 = 480
\]
\[
-2.50x = 480 - 530
\]
\[
-2.50x = -50
\]
\[
x = \frac{-50}{-2.50} = 20
\]

Now, substitute $ x = 20 $ into the first equation to find $ y $:
\[
x + y = 100
\]
\[
20 + y = 100
\]
\[
y = 100 - 20 = 80
\]

### Final Answer:
- 20 pounds of peanuts,
- 80 pounds of cashews.

Would you like more details or have any questions? 

Here are some related questions to explore further:
1. What would happen if the price per pound of peanuts increased?
2. How would the mix change if the total weight was 150 pounds?
3. How can we adjust the system if the price of cashews changed?
4. What if the mix was required to cost $5.00 per pound?
5. How would we solve if the proportion of peanuts and cashews was fixed?

**Tip:** Always double-check your equations by plugging the solution back into the original problem to verify the result.

A nut wholesaler sells a mix of peanuts and cashews. He charges $2.80 per pound for peanuts and $5.30 per pound for cashews. If the mix is to sell for $4.80 per pound, how many pounds each of peanuts and cashews should be used to make 100 pounds of the mix?

Discover how to solve a system of equations to determine the quantity of peanuts and cashews in a 100-pound nut mix priced at $4.80 per pound. This problem uses key algebraic concepts and involves solving linear equations. Ideal for students in Grades 9-11.

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