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?

The system of linear equations which could be used to solve for the number of each ticket type sold are :

Ticket types :

Ticket cost :

The total amount made from tickets sales :

35a + 25b + 15c = 37500

From (1) :

35(5c) + 25b + 15c = 37500

175c + 25b + 15c = 37500

190c + 25b = 37500 - - - - - (2)

Sales from Mezzanine tickets only = 25b

25b = 4(15c)

25b = 60c - - - - (3)

Therefore, the system of linear equation required to solve the problem are equations (2) and (3)

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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

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step-by-step explanation: