A circus performance is scheduled in Memorial Auditorium and

A circus performance is scheduled in Memorial Auditorium, and the reserved - seat tickets are to cost twice as much as the regular admission seats. There are 1,000 reserved sets and a total seating capacity of 12,000 in The auditorium. What price should be charged for each type of ticket so that a capacity crowd will yield $91,000 in ticket sales?

Solution

Please note from the question

1. Number of Reserved seat = 1000

2. Total Number of seats = 12000

3. Number of Regular seat = 12000 - 1000 = 11000

Lets consider Cost of a Reserved seat to be x and Cost of a Regular seat to be y.

As Cost of reserved seat = 2*Cost of Regular seat,

Thus x = 2*y.

Also, We have been give Total ticket sale money = 91000 dollars

Thus, 1000*x + 11000*y = 91000

By using x=2*y and 1000*x+11000*y = 91000 equations.

we find, 1000*2*y + 11000*y = 91000

which implies y*(2000+11000) = 91000 , y = 91000/13000 , y = 7

Thus x = 2*7 = 14.

Thus, Cost of Reserved seat is 14 dollars and Cost of Regular seat is 7 dollars