The 2842-seat performing arts center has three sections-orchestra, mezzanine, and balcony. The mezzanine has one-sixth fewer seats than the orchestra. How many seats are in the balcony if the orchestra has 1,218 seats?
Please show me how to set up the equation....
thanks
All the seats must add up to 2842. The orchestra has 1218. The mezzanine has 1/6 fewer or 5/6 of the value of the orchestra. The seats in the balcony are your unknown.
2842 = 1218 + (5/6) 1218 + X
I hope this helps. Thanks for asking.
To set up the equation, you first need to find the number of seats in the mezzanine section.
Given that the orchestra section has 1,218 seats, let's represent the number of seats in the mezzanine as 'x'.
Since the mezzanine has one-sixth fewer seats than the orchestra, you can calculate it by subtracting one-sixth of the orchestra seats from the total.
To find one-sixth of the orchestra seats, you can divide the number of orchestra seats by 6:
(1/6) * 1,218 = 203
Now, you can represent the number of seats in the mezzanine section as:
x = 1,218 - 203
Simplifying the equation,
x = 1,015
This means that there are 1,015 seats in the mezzanine section.
Lastly, to find the number of seats in the balcony, you subtract the total number of seats in the orchestra and the mezzanine sections from the total capacity of the performing arts center.
2842 - 1,218 - 1,015 = 609
Therefore, there are 609 seats in the balcony section.