Question

A high school prom costs the school $6,160 to put on. Tickets are sold for $40 per single attendee or $70 per couple. If an equal number of singles' and couples' tickets are sold, a

minimum of how many people in total must attend the prom to cover its costs?
A) 56
B) 84
C) 112
D) 168

Answer 1

* The cost of the prom is $6,160

* Tickets are $40 for a single attendee or $70 for a couple (2 people)

* Let's break this down:

* If x people attend as singles, they will buy x tickets at $40 each, so they contribute x * $40 to the revenue

* If x people attend as couples, there are 2x people total who buy x tickets at $70 each, so they contribute x * $70 to the revenue

* Since an equal number attend as singles and couples, x must be the same in both cases

* We need:

* x * $40 (revenue from singles) + x * $70 (revenue from couples) >= $6,160 (cost of prom)

* x * $40 + x * $70 >= $6,160

* x * ($40 + $70) >= $6,160

* x * $110 >= $6,160

* x >= 6,160/110

* x >= 56

* Therefore, the minimum number of people who must attend is 56.

The answer is A.