Question

Suppose you’re managing a theater and you need to know how many adults and children are in attendance at a show. The auditorium is sold out and contains a mixture of adults and children. The tickets cost $23 per adult and $15 per child, and the auditorium has 250 seats. The total ticket revenue for the event is $4,846. How many adults and children are in attendance?

Answer 1

To find the number of adults and children in attendance at a theater show, we can set up and solve a system of linear equations using the given total ticket revenue, the price of adult and child tickets, and the total number of seats.

Step-by-step explanation:

The question involves determining the number of adults and children attending a theater show when the total revenue and ticket prices for adults and children are known, as well as the total number of seats. This is a typical linear algebra problem, often solved using a system of equations. We are given the following information:

• Total number of seats: 250
• Adult ticket price: $23
• Child ticket price: $15
• Total ticket revenue: $4,846

We set up two equations to represent the situation:

1. A + C = 250 (where A represents the number of adult tickets and C represents the number of child tickets)
2. 23A + 15C = $4,846

We can solve these equations using substitution or the elimination method to find the values of A and C. After solving the system of equations, we find that:

• Number of adult tickets sold: 166
• Number of child tickets sold: 84