With a student body card, tickets to the football game cost $1.00. Without a car

Question

With a student body card, tickets to the football game cost $1.00. Without a card, the price was $6. At the new computerized gates, each fan deposited his or her ticket to open the gate. As each gate reported a running total was kept on a central computer. The computer was programmed to count the number of people who entered and keep a running total for the cost of the tickets. For the season opener, the total number of tickets was 12,438 and the total revenue was $36,798. The University is pressuring the athletic director to raise the price of tickets. The athletic director needs to know how many tickets of each type were sold.

Explanation / Answer

Solution:

Given that

a.) Price of ticket without student body card = $ 6 =a
b.) Price of ticket with student body card (reduced ticket)= $ 1 =b
total numbed of ticket sold = 12 438 =c

and
revenue generated = $ 36,798 in total =d

d = a x ( c - N ) + b x N
d = ac - aN + bN
d = ac + N (b - a)
N = ( d - ac ) / ( b - a )
N = ( 36 798 - 6 x 12 438 ) / -5
N = -37830 / -5 = 7566

Total number of 7 566 student body card tickets at $ 1 = $ 7 566

Reamining tickets without body card = 12 438 - 7 566 = 4872

and revenue form 4 872 tickets at $ 6 = $ 29 232

Answer:

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