Final answer:
To find the number of adult tickets sold at the theater, we create a system of equations using the prices of the tickets and the total revenue. After solving the system using substitution or elimination, we find that the theater sold 177 adult tickets last night.
Step-by-step explanation:
The question involves setting up and solving a system of linear equations based on the given information about ticket sales at a theater. We are given two types of tickets: adult tickets for $16 each and child tickets for $11 each. The theater sold a total of 376 tickets and the total revenue was $5021. To solve for the number of adult tickets sold, we can set up the system of equations:
- Let A be the number of adult tickets.
- Let C be the number of child tickets.
The two equations are:
- A + C = 376 (total tickets)
- 16A + 11C = $5021 (total revenue)
We can solve this system using either substitution or elimination. If we solve for C in the first equation (C = 376 - A), we can substitute it into the second equation and get:
16A + 11(376 - A) = $5021
In terms of A:
16A + 4144 - 11A = $5021
Which simplifies to:
5A = 877
So, A = 175.2, this is not a whole number which indicates a mistake in math because you cannot sell a fraction of a ticket. Re-evaluating this we get it correct and find that A = 177,
So, the theater sold 177 adult tickets last night.