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The image shows a math problem about pricing walnuts and pecans at an organic nut shop. Here's the problem you shared:

**Problem:**
A customer buys 5 pounds of walnuts and 3 pounds of pecans for $21. Another customer buys 4 pounds of walnuts and 5 pounds of pecans for $28.50. The task is to find the cost per pound of pecans.

Let’s define variables:
- Let $ w $ be the price of one pound of walnuts.
- Let $ p $ be the price of one pound of pecans.

We now have two equations:
1. $ 5w + 3p = 21 $
2. $ 4w + 5p = 28.50 $

### Step-by-Step Solution:

1. **From the first equation:**
   \[ 5w + 3p = 21 \]
   
2. **From the second equation:**
   \[ 4w + 5p = 28.50 \]

We can solve this system of equations using substitution or elimination.

### Using Elimination Method:
Multiply the first equation by 4 and the second equation by 5 to eliminate the $ w $ term:

- $ 20w + 12p = 84 $
- $ 20w + 25p = 142.50 $

Now subtract the first equation from the second:
\[
(20w + 25p) - (20w + 12p) = 142.50 - 84
\]
This simplifies to:
\[
13p = 58.50
\]
\[
p = \frac{58.50}{13} = 4.50
\]

Thus, the cost of one pound of pecans is **$4.50**.

Would you like more details or have any questions? Here are some related problems to try:

1. What is the cost of one pound of walnuts?
2. How much would 2 pounds of walnuts and 4 pounds of pecans cost?
3. What is the total cost if a customer buys 10 pounds of pecans?
4. What is the difference in total cost if a customer buys 3 pounds of walnuts versus 3 pounds of pecans?
5. How much would 3 pounds of walnuts and 6 pounds of pecans cost?

**Tip:** When solving systems of equations, always check if elimination or substitution makes the process simpler based on the given numbers.

Amy owns an organic nut shop. A customer buys 5 pounds of walnuts and 3 pounds of pecans for $21. Another customer buys 4 pounds of walnuts and 5 pounds of pecans for $28.50. What is the cost of one pound of pecans?

Learn how to find the cost of one pound of pecans by solving a system of equations. This problem involves algebraic concepts, including setting up and solving linear equations using the elimination method. Suitable for students in Grades 8-10.

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