Let's solve the problem step by step.

Define Variables:

• Let $x$ represent the weight of dry roasted peanuts (in ounces).
• Since the total weight of the trail mix is 20 ounces, the weight of dried cranberries will be $20 - x$ ounces.

Price Assumptions:

• Let the price per ounce of dry roasted peanuts be $P_p$ (in dollars).
• Let the price per ounce of dried cranberries be $P_c$ (in dollars).

Total Cost Equation:

Luke wants to spend $11 on 20 ounces of trail mix. Therefore, the total cost can be expressed as: $P_p \cdot x + P_c \cdot (20 - x) = 11$

Now, we need to know the prices per ounce of peanuts ($P_p$) and cranberries ($P_c$) to continue. Could you provide those prices or clarify any additional details?

Let me know if you'd like further clarification or details.

Related Questions:

1. What are the common prices of peanuts and cranberries per ounce in your area?
2. How would the solution change if Luke had a different budget, say $15?
3. What if Luke wanted to mix equal weights of peanuts and cranberries, how would the total cost change?
4. How could the weight distribution be changed if the prices of peanuts and cranberries are very different?
5. Can you think of a situation where mixing different amounts of these ingredients would reduce the total cost?

Tip: In word problems, clearly identifying all variables and relationships helps in setting up the correct equation to solve the problem.