Final answer:
The maximum number of people STUCO can accommodate with $32,000 is found by solving the equation 1750 + 14x = 32000, which results in just over 2160 people. Thus, the closest and correct answer is 2000 people.
Step-by-step explanation:
The student's question involves solving a linear equation to find the greatest number of people that the Student Council (STUCO) can accommodate with a budget of $32,000 from ticket sales, considering the costs for cleanup and security. A fixed cleanup fee of $750 and a security fee of $1,000 are added to the variable cost of $14 per person attending the event.
Let x represent the number of people that can be accommodated. The total cost for x people can be represented by the equation 750 + 1000 + 14x = 32000. Combining the fixed costs, we get 1750 + 14x = 32000. Now, we solve for x by subtracting 1750 from both sides, giving us 14x = 30250. Lastly, we divide both sides by 14 to find x, which results in approximately 2160 people. This means that choice B. 2200 people is not possible, and the greatest number of people STUCO can accommodate is slightly less than 2200, making option A. 2000 people the correct answer.