Problema Solution
Tickets to a school dance cost $4 and the projected attendance is 300 people. It is further projected that for every 10ยข increase in ticket price the average attendance will decrease by 5. At what ticket price will the receipts from the dance be $1,248
Answer provided by our tutors
Let x = the number of increases, x>0
Ticket price = ( 4 + .1x ), because you're considering a 10 cent increase at a time.
Attendance = ( 300 - 5x ), because you're considering a 5 person decrease each time you increase the ticket price by 10 cents.
To get the revenue (receipts) we multiply the number of people attending times the amount of tickets sold, or ( 300 - 5x ) * ( 4 + .1x), and get:
( 4 + 0.1x )*(300 - 5x) = 1248
0.5x^2 - 10x + 48 = 0
x^2 - 20x + 96 = 0
by solving we find
x1 = 8
x2 = 12
click here to see the step by step solution of the equation
4 + 0.1*8 = $4.8
4 + 0.1*12 = $5.2
for the ticket price of $4.8 and $5.2 the receipts from the dance will be $1,248.