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.

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JeanaShupp JeanaShupp · Answer 1 · 2018-10-22T09:31:07+02:00

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.