Question

Please help, having a hard time

Answer 1

C

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

`400 * price \: of \: orchestra \: seat \: + \: 250 * price \: of \: balcony \: seat \: = 8250`

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.

Answer 2

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

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.