An opera house has two kinds of seats, orchestra and mezzanine. The total amount the opera house made in ticket sales for a show last Saturday was $137,000. They sold a total of 1,100 mezzanine tickets at $70 a ticket. They sold 500 orchestra tickets. If t represents the cost of an orchestra ticket, write an equation representing this situation and complete the statement that follows.

Answer:1) The required equation 77000+500t=137000

2) Cost of 1 orchestra ticket is $12.

Step-by-step explanation:

The total amount the opera house made in ticket on Saturday = $137000

No. of mezzanine tickets they sold = 1100

cost of 1 mezzanine ticket = $70

∴cost of 110 mezzanine tickets=1100*70 = $77000 ... (1)

Now let t be the cost of orchestra ticket then

cost of 500 tickets = 550*t=$500t ... (2)

Adding (1) and (2) is equal to the total sales, so the required equation 77000+500t=137000

⇒500t=137000-77000 (subtract 77000 on both sides)

⇒500t=6000⇒t=12 (dividing 500 from both sides)

∴ Cost of 1 orchestra ticket is $12.