The Equation

Question

The equations 5x + 2y = 76 and 3x + 2y = 40 represent the money collected from movie sales during one showing. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket?

Answer 1

Hi Star-Asia,

 

Let's begin by summarizing our given info and then solve for our unknown (x):

 

     x = cost of adult ticket

     y = cost of student ticket

 

     Equation #1:  5x + 2y = 76 (money collected)

     Equation #2:  3x + 2y = 40 (money collected)

 

     Equation #3:  Equation #1 - Equation #2

                         [eliminates unknown (y) ]

     Equation #3:  3x = 36

                           x = 36/12

                           x = $3 (cost of adult ticket)

 

This solution demonstrates the Elimination Method for solving a system of simultaneous linear equations.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.