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Answer:

The balcony seat costs $9,  the orchestra seat costs $9 + $6 = $15.

Step-by-step explanation:

Let x is the cost/price of one balcony seat, in dollars.

Then the cost of one orchestra seat is (x+6) dollars, according to the condtion.

The total cost of tickets is  

250x + 400*(x+6) = 8250.

Simplify it step by step.

250x + 400x + 2400 = 8250,

650x = 8250 - 2400 = 5850  ====>  x = 5850/650 = 9.

Answer.  The balcony seat costs $9,  the orchestra seat costs $9 + $6 = $15.

Check.   9*250 + 15*400 = 8250.  Correct.

Answer:

C

Step-by-step explanation:

Let x = price of one balcony seat and y = price of one orchestra seat

Price of orchestra seat = Price of balcony seat + 6

Or y = x + 6

[tex]400 \times price \: of \: orchestra \: seat \: + \: 250 \times price \: of \: balcony \: seat \: = 8250[/tex]

Or 400y + 250x = 8250

Now that we have to two equations with two variables, we can use either substitution, elimination or graphing to find the prices of the seats.

I attached a picture of the graph. Remember since we set y as the price of the orchestra seat, the y coordinate in the point of intersection will be the price for one orchestra seat. This will be the same for the price of a balcony seat and the x coordinate.

Therefore, the price of one balcony seat is $9 and the price of one orchestra seat is $15.

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