https://file.aiquickdraw.com/mathbot/file/1726973893878wv068mc2.jpg

The problem shown in the image asks to solve the following:

Ned, the owner of Ned's Nut Shop, sells peanuts for $10 per pound and cashews for $9 per pound. Ned wants to create a 20-pound barrel of mixed nuts and sell it for $9.55 per pound. The task is to determine how many pounds of peanuts and cashews should be mixed.

Let:
- $ x $ = pounds of peanuts
- $ y $ = pounds of cashews

### System of Equations:
1. The total weight of the mixture is 20 pounds:
   \[
   x + y = 20
   \]

2. The total cost of the mixture per pound must average to $9.55. So, the total cost for 20 pounds must be:
   \[
   10x + 9y = 9.55 \times 20
   \]
   Simplifying the right-hand side:
   \[
   10x + 9y = 191
   \]

Now we have the system of equations:
1. $ x + y = 20 $
2. $ 10x + 9y = 191 $

### Solving the system:
From the first equation, solve for $ x $:
\[
x = 20 - y
\]

Substitute this into the second equation:
\[
10(20 - y) + 9y = 191
\]
\[
200 - 10y + 9y = 191
\]
\[
200 - y = 191
\]
\[
y = 200 - 191 = 9
\]

Now substitute $ y = 9 $ back into $ x + y = 20 $:
\[
x + 9 = 20 \quad \Rightarrow \quad x = 11
\]

### Final Answer:
Ned should mix **11 pounds of peanuts** and **9 pounds of cashews** to make a 20-pound blend that sells for $9.55 per pound.

Would you like any more details, or do you have further questions?

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Here are 5 related questions:
1. How would the solution change if the price per pound for peanuts was $11?
2. Can you solve this problem using substitution or elimination methods?
3. How would the system of equations change if Ned wanted to create 25 pounds of the mixture?
4. What if Ned wanted the mix to sell for $9.60 per pound?
5. How can this problem be visualized graphically?

**Tip:** When solving a system of equations, always simplify one equation first before substituting it into the other for easier calculations!

Ned, the owner of Ned's Nut Shop, sells peanuts for $10 per pound and cashews for $9 per pound. Ned wants to create a 20-pound barrel of mixed nuts and sell it for $9.55 per pound. How many pounds of peanuts and cashews should Ned use?

Solve the system of equations for mixing peanuts and cashews at Ned's Nut Shop. Learn how to calculate the mixture for a 20-pound blend selling at $9.55 per pound, using basic algebraic techniques.

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