Let the number of pounds of cashews be $x$ and the number of pounds of peanuts be $y$.

Set up the system of equations:

1. The total weight of the cashews and peanuts is 11 pounds: $x + y = 11$

2. The total cost of the cashews and peanuts is $31. Cashews cost $3.00 per pound and peanuts cost $2.50 per pound: $3x + 2.5y = 31$

Solve the system of equations:

Step 1: Solve the first equation for $y$: $y = 11 - x$

Step 2: Substitute $y = 11 - x$ into the second equation: $3x + 2.5(11 - x) = 31$ Simplify the equation: $3x + 27.5 - 2.5x = 31$ Combine like terms: $0.5x + 27.5 = 31$ Subtract 27.5 from both sides: $0.5x = 3.5$ Solve for $x$: $x = \frac{3.5}{0.5} = 7$

Step 3: Substitute $x = 7$ into the equation $y = 11 - x$: $y = 11 - 7 = 4$

Conclusion:

There are 7 pounds of cashews and 4 pounds of peanuts in the order.

Would you like more details on how to solve this? Or do you have any other questions?

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Here are some related questions to explore further:

1. What happens if the price of cashews increases to $4 per pound?
2. How would the problem change if the total weight were 12 pounds instead of 11?
3. How would you set up a similar problem for a different pair of items, like almonds and walnuts?
4. If you were to graph the system of equations, how would the lines look?
5. How can this type of system be solved using matrix methods?

Tip: Always start by expressing one variable in terms of the other to reduce the number of variables in the system.