Question

A theater is showing a ballet performance. Tickets are available for three levels in the performance hall. Lower level tickets cost $35, mezzanine tickets cost $25, and upper balcony tickets cost $15. For a certain performance the theater sold 5 times as many lower level tickets as balcony tickets. The theater sold $37,500 in tickets that performance. The money made from mezzanine tickets alone was 4 times the money made from balcony tickets.
Which system of linear equations could be used to solve for the number of each type of ticket sold?

Answer 1

Answer: 25y= 60x

190x +25y= 37500

Step-by-step explanation:

Let x = Number of balcony tickets.

then, Number of lower level tickets  = 5x

Let y = Number of mezzanine tickets

Money made from ,

balcony tickets = 15x

lower level tickets = 35 (5x) = 175 x

mezzanine tickets = 25y

Money made from mezzanine tickets=  4 x( money made from balcony tickets.)

⇒ 25y = 4 (15x)

⇒ 25y= 60x              (i)

Also, total cost of the tickets = 15x+175x+25y = 37500

⇒ 190x +25y= 37500          (ii)

From (i) and (ii), the system of linear equations could be used to solve for the number of each type of ticket sold:

25y= 60x

190x +25y= 37500