Final answer:
The set of solutions for the amount spent at the fall festival craft show can be found by setting up and graphing inequalities based on the given budget constraint. The feasible region on the graph will represent all the possible combinations of spending that do not exceed the budget limit.
Step-by-step explanation:
To determine the set of solutions (amount spent on each item) for you and your friend at the fall festival craft show, we should look at the budget constraint similar to the ones described for Marie and Alphonso. Marie has a weekly budget of $24, which she spends on magazines and pies. This constraint means that the total amount spent on both items cannot exceed $24. The solutions for the amount she can spend on each item are all the combinations of magazine and pie prices that add up to $24 or less.
In Alphonso's case, he also has a budget constraint and can choose any combination of bus tickets and burgers that falls on or inside his budget constraint. We can graph this constraint by plotting the maximum number of each item he can afford if he only bought that item and drawing a line (or curve) to connect these points. Every combination along this line represents a mix of burgers and bus tickets that he can afford without exceeding his budget.
Applying this concept to your situation, if we assume your budget is similar to Option D, being $20 in total at the craft show, you would need to set up the inequalities representing your spending limit for each item and graph the inequalities to find the solution set. This involves graphing a line where the x-axis represents the amount spent on one item, and the y-axis represents the amount spent on the other item, with the total not exceeding $20. The feasible region that lies on or below this line would represent all the combinations of spending on the two items within your budget. So the correct answer is: B) Set up and graph the inequalities to find the solution.