The Valley High School student council is planning a dance. The school has 200 students. The lowest possible ticket price is $1.00, and they estimate that for every $0.50 increase in ticket price, 25 fewer students will attend. What ticket price will maximize the student council’s profit?


  1. The maximum revenue is $312.50 for 125 students
    What number of students would attend at the lowest ticket  price?
    At the lowest ticket  price of $1.00 it is likely that all the 200 students would attend because it is the most affordable price
    revenue for 200 students=$1.00*200
    revenue for 200 students=$200.00
    When ticket price increases to $1.50,there would reduction in attendance by 25 students, leaving only 175 students
    revenue for  175 students=$1.50*175
    revenue for 175 students=$262.50
    When the ticket price increases to $2.00 from $1.50, the attendance would reduce to 150
    revenue for 150 students=$2.00*150
    revenue for 150 students=$300.00
    When the ticket price increases to $2.50, only 125 students would grace the event
    revenue for 125 students=$2.50*125
    revenue for 125 students=$312.50
    When the ticket price increases to $3.00, only 100 students would be in attendance
    revenue for 100 students=$3.00*100
    revenue for 100 students=$300.00
    At this point, the revenue has started declining, hence, the maximum revenue is $312.50 for 125 students
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