TICKETS Three kinds of tickets are available for a concert: orchestra seating, mezzanine seating, and balcony seating. The orchestra tickets cost $2 more than the mezzanine tickets, while the mezzanine tickets cost $1 more than the balcony tickets. Twice the cost of an orchestra ticket is $1 less than 3 times the cost of a balcony ticket. Determine the price of each kind of ticket.

an orchestra seating ticket cost $10

A mezzanine seating ticket cost $8

A balcony seating ticket cost $7

Step-by-step explanation:

Let x represent the price of an orchestra seating ticket.

Let y represent the price of a mezzanine seating ticket.

Let z represent the price of a balcony seating ticket.

The orchestra tickets cost $2 more than the mezzanine tickets. It means that

x = y + 2- - - - - - - 1

The mezzanine tickets cost $1 more than the balcony tickets. It means that

y = z + 1 - - - - - - -2

Twice the cost of an orchestra ticket is $1 less than 3 times the cost of a balcony ticket. It means that

2x = 3z - 1- - - - - - - - -3

Substituting equation 2 into equation 1, it becomes

x = z + 1 + 2

x = z + 3 - - - - - - - - - -4

Substituting equation 4 into equation 3, it becomes

2(z + 3) = 3z - 1

2z + 6 = 3z - 1

3z - 2z = 6 + 1

z = 7

x = z + 3 = 7 + 3

x = 10

y = z + 1 = 7 + 1

y = 8

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