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.