Quantities and Modeling (Please Help!!!)

Question

That's the ticket!

There are 40 rows of seats in the Varsity Theater, with 20 seats in each row. During regular performances, all seats cost $12.

 

A movie rents for $275 per performance. 

 

For a special movie premiere, the theater owner decided to charge $20 per ticket for the first r rows of the theater and $15 for the remaining rows.

 

Explain how you could find the owner's total income if you knew the value of r and you knew that all of the tickets were sold. 

Answer 1

This question is asking you write income as a function of r, assuming that the theater is sold out. 

 

Since there are 20 seats per row, the income generated for selling one row of seats at $20 per seat is equal to: 

 

$20/seat * 20 seats/row = $400/row

 

Since r denotes the number of rows where tickets are $20/seat, the income generated from r rows of seats is $40*r

 

The income generated for selling one remaining row of seats at $15 per seat is equal to:

 

$15/seat * 20 seats/row = $300/row

 

Since we assumed a sell-out of the theater, the number of rows sold remaining is equal to the total number of rows minus the amount of rows sold at $20 per set (which is r): 40 - r

 

Thus, the total amount of income generated from the seats is as following (don't forget to include the cost of the movie performance)

 

i = $400*r + $300 * (40-r) - $275

 

By plugging in any given value of r, you will obtain the income. I hope this helped!

 

If you found this helpful and would like a more in-depth breakdown of how I set up the equations, please contact me so we can set up a tutoring lesson!