Equations and Matrice

Question

Use the information from the box office to set up a system of equations?

Solve the system of equations to identify how many of each type of ticket was sold?

The theater you work for has a total of 500 seats and sells three different types of tickets:

1. adult tickets for $8
2. senior citizen tickets for$7
3. child tickets for $5

The box office states that the ticket sales for Saturday came to $3,269 and that the theater was sold out. They also tell you that there was exactly 77 senior citizen tickets sold.

Answer 1

Let x = number of adult tickets

Let y = number of senior tickets

Let z = number of child tickets

x+y+z=500 Since there are 500 seats

8x+7y+5z=3269 from the ticket sales data

y=77

Solving this using the calculator for the following matrix

[1 1 1 500]

[8 7 5 3269]

[0 1 0 77]

x=205

y=77

z=218