Final answer:
If the auditorium is filled to capacity, the school will earn $3600 from ticket sales. The number of adult attendees is 200, and the number of student attendees is 600. The cost of adult tickets is $6 and the cost of student tickets is $4.
Step-by-step explanation:
To determine the amount of money that will be earned if the auditorium is filled to capacity, we need to calculate the number of adult and student attendees at this year's play. Last year, three times as many students attended as adults. Let's assume that the number of adult attendees is 'x'.
This means that the number of student attendees will be 3 times 'x', which is 3x.
The total number of attendees is the sum of adult and student attendees, which is x + 3x = 4x.
Since the auditorium has a seating capacity of 800, we can set up the equation 4x = 800 to solve for x.
Dividing both sides of the equation by 4, we find that x = 200.
So there will be 200 adult attendees and 3 times that, which is 600 student attendees.
Now, to determine the amount that will be earned, we multiply the number of adult attendees by the cost of adult tickets and the number of student attendees by the cost of student tickets, and then add the two amounts.
The amount earned from adult tickets is 200 * $6 = $1200.
The amount earned from student tickets is 600 * $4 = $2400.
The total amount earned from ticket sales if the auditorium is filled to capacity is $1200 + $2400 = $3600.