Tickets sold to a school dance cost $4 and the projected attendance is 300. for every $0.10 increase in price the attendance will decrease by 5. what ticket price will generate $1237.5?

1 Answer
Aug 8, 2016

Answer:

#$4.50 or $5.50#

Explanation:

Attendance (A) given by:

#A = 300 - 5n# where #n# is every $0.10 over $4.

Ticket price (T) given by:

#T = 4 + 0.1n#

Total earnings (E) given by:

#E = A*T#

#E= (300-5n)(4+0.1n)#

#E = 1200 + 30n - 20n - 0.5n^2 = 1200 + 10n - 0.5n^2#

We want #E = 1237.5# so

#1237.5 = 1200 + 10n - 0.5n^2#

Yielding a quadratic:

#0.5n^2 - 10n + 37.5 = 0#

Multiply by 2 to get tidier numbers. This is not really necessary, just out of preference.

#n^2 - 20n + 75 = 0#

Could easily factorise by eye but will use quadratic formula for completeness.

#n = (20+-sqrt((-20)^2 - 4(1)(75)))/2#

#n = (20+-sqrt(400 - 300))/2 = (20+-10)/2 = 15 or 5#

#n = 5 implies T = $4.50#

#n = 15 implies T = $5.50#