Theater Attendance and Ticket Sales

The video tutorial explains how to solve a problem involving a movie theater filled to capacity with 350 people, where ticket prices vary for children, students, and adults. The problem involves setting up a system of equations based on the given conditions, such as the total ticket sales amounting to $2,415 and the number of adults being half the number of students. The tutorial guides through assigning variables, formulating equations, and solving the system using substitution to find the number of children, students, and adults in the theater.

What is the total capacity of the movie theater?

• 350

• 300

• 450

• 400

How much does a student ticket cost?

• $4.50

• $12.50

• $7.50

• $10.50

If X represents the number of children, what does Y represent?

• Number of seats

• Number of tickets

• Number of students

• Number of adults

What is the equation for the total number of people in the theater?

• X + Y + Z = 300

• X + Y + Z = 450

• X + Y + Z = 350

• X + Y + Z = 400

What is the relationship between the number of adults and students?

• Z = Y

• Z = 2Y

• Y = 2Z

• Y = Z

After substitution, what is the first equation with two variables?

• X + 3Z = 350

• X + 2Z = 350

• X + 4Z = 350

• X + 5Z = 350

What is the value of Z, representing the number of adults?

• 50

• 60

• 80

• 70

How many students attended the theater?

• 130

• 100

• 110

• 120

What is the total number of children in the theater?

• 150

• 160

• 170

• 180

What is the total ticket sales amount?

• $2,000

• $2,500

• $2,750

• $2,415