Final answer:
To stay within the $2,000 budget for Mark and Heather Starr's reception, we subtract the $50 cleanup fee and divide the remaining $1,950 by $38 per person. Rounding down, the greatest number of people they can invite is 51.
Step-by-step explanation:
The student has asked about the maximum number of people that can be invited to a reception given a budget constraint. This is a mathematics problem involving basic arithmetic, specifically budget allocation. To stay within their budget of $2,000, we must subtract the flat cleanup fee from the total budget and then divide the remaining amount by the cost per person. The cleanup fee is $50, so:
Total budget for guests = Total budget - Cleanup fee
Total budget for guests = $2,000 - $50
Total budget for guests = $1,950
Next, we divide the remaining budget for guests by the cost per person, which is $38:
Number of people = Total budget for guests / Cost per person
Number of people = $1,950 / $38
Number of people = 51.3158...
Since you cannot invite a fraction of a person, we round down to the nearest whole number, which means the greatest number of people they can invite is 51. So, the answer is C) 51.