Final answer:
By dividing Marie's total budget for the retirement party by the cost per guest, we find that the maximum number of guests Marie can invite is 9.
Step-by-step explanation:
The student's question asks us to determine the maximum number of guests Marie can invite to her retirement party if the cost is directly proportional to the number of guests and she has a budget of $18. If inviting 4 guests costs $8, then we can determine the cost per guest by dividing $8 by 4, which gives us $2 per guest. Given that Marie can spend a total of $18 for her party, to find the maximum number of guests, we divide her budget by the cost per guest:
$18 ÷ $2 per guest = 9 guests
Therefore, Marie can invite a maximum of 9 guests to her retirement party.