Solving Equations Application

A movie theater charges $10 for each adult ticket and $5 for each child ticket. At a showing where 150 tickets were sold, the theater collected $1200. How many child and adult tickets were sold?

• There were 90 adult tickets and 60 child tickets sold.

• There were 60 adult tickets and 90 child tickets sold.

• There were 50 adult tickets and 40 child tickets sold.

• There were 40 adult tickets and 50 child tickets sold.

Identify the number of solutions for the system of equations: 2x + 3y = 8 and 4x + 6y = 16.

• Infinite solutions

• No solution

• One solution

• Two solutions

Graph the system of equations: x + y = 5 and 2x - y = 3. Identify the point of intersection.

• (1, 4)

• (2, 3)

• (4, 1)

• (3, 2)

Solve the system of equations by substitution method: 3x - 2y = 7 and 5x + 4y = 11.

• x = 3, y = -2

• x = 2, y = 3

• x = 5, y = 2

• x = -1, y = 4

A movie theater sells adult tickets for $10 each and child tickets for $6 each. If a total of 100 tickets were sold for $800, write a system of equations to represent this scenario and solve for the number of adult and child tickets sold.

• The number of adult tickets sold is 60, and the number of child tickets sold is 40.

• The number of adult tickets sold is 80, and the number of child tickets sold is 20.

• The number of adult tickets sold is 50, and the number of child tickets sold is 50.

• The number of adult tickets sold is 70, and the number of child tickets sold is 30.

Identify the number of solutions for the system of equations: 3x - 2y = 5 and 6x - 4y = 10.

• No solution

• Two solutions

• Infinite solutions

• One solution

Graph the system of equations: 2x + y = 4 and x - y = 1. Identify the point of intersection.

• (1, 4)

• (3, 2)

• (5, 1)

• (2, 3)

Solve the system of equations by substitution method: 4x - 3y = 10 and 2x + y = 5.

• x = 2, y = 1

• x = 5, y = 3

• x = 1, y = 4

• x = 3, y = 2

The length of a rectangle is 4 inches more than twice its width. If the perimeter of the rectangle is 38 inches, what is the width?

Adam, Julius, and Mike volunteered to read to children at a public library. Julius worked two hours less than Mike. Adam worked twice as many hours as Julius. Altogether they worked 58 hours. How many hours did Adam work?

• 20 hours

• 14 hours

• 16 hours

• 28 hours