Final answer:
The system of equations to be set up is x + y = 300 to account for the seat capacity and 12x + 7y = 2700 to meet the revenue goal. These equations will help find the number of adult and student tickets to sell.
Step-by-step explanation:
The choir is facing a common issue in theater economics: maximizing revenue with a limited number of seats and performances. To answer this question, we need to construct a system of equations to determine the number of adult (x) and student (y) tickets to sell. Given that adult tickets are priced at $12 and student tickets at $7, and the theater has a seating capacity of 300, the first equation is derived from the total seat limit:
x + y = 300
We add the number of adult tickets to the number of student tickets, which should equal the total number of seats available.
The second equation represents the revenue goal:
12x + 7y = 2700
The choir needs to raise $2700 in total, so we multiply the number of adult tickets by their price and add it to the number of student tickets multiplied by their price.
Together, these two equations, x + y = 300 and 12x + 7y = 2700, form the system of equations needed to solve the problem, applying similar steps as in the budget constraint equation used in other financial scenarios.