The Correct Answer and Explanation is:
The correct answer is 82 students.
To determine how many students attended the dance, we must first understand the two components of the total cost. The total payment of $325 consists of a fixed, one-time fee and a variable fee that depends on the number of attendees. The fixed fee is the $120 cost to rent the building. The variable fee is the $2.50 charge for each student.
The initial step is to isolate the portion of the total cost that was applied to the students. We can achieve this by subtracting the fixed building rental fee from the total amount Ava paid. The calculation would be the total payment of $325 minus the $120 rental fee. This leaves us with $205. This $205 represents the total amount of money paid specifically for the students who attended the dance, separate from the cost of the venue itself.
Now that we know the total amount spent on students was $205, and we know that the cost for each individual student was $2.50, we can calculate the number of students. To do this, we need to divide the total student cost by the per-student cost. So, we divide $205 by $2.50. This calculation gives us a result of 82.
Therefore, 82 students attended the school dance. We can verify this answer by working backward. If 82 students each cost $2.50, the total variable cost is 82 multiplied by $2.50, which equals $205. Adding the fixed rental cost of $120 to this variable cost gives us a grand total of
325(325(205 + $120). This final number matches the total amount Ava paid, confirming that our calculation is correct and that 82 students were at the dance.
