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

Answer 2

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

• 25b = 60c
• 190c + 25b = 37500

Ticket types :

• Lower level = a
• Mezzanine = b
• Upper balcony = c

• a = 5c - - - - (1)

Ticket cost :

• Cost of a = $35
• Cost of b = $25
• Cost of c = $15

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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