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Question

A music festival usually attracts 500 people at a cost of $12/person. For every $1 rise in the admission price, 25 less people attend the festival. If y is the total amount of takings and x is the number of $1 increases, find the function which gives y in terms of x.

Answer 1

The total amount of takings equals the amount of people that attend the festival multiplied by the price of admission. 

Without any adjustments it would just be: 

Y (total, in $)= ($12)(500)

 

However you need to take into account the change in ticket price. The $1 increase(s) would be in addition to the $12 so this becomes ($12+1x) or just (12+x) 

For each $1 increase, it will mean 25 fewer people than the 500 attendees. This becomes (500-25x)

 

The correct equation is: 

Y= (12+x)(500-25x)  Which simplifies to:

Y=6000+200x-25x²  OR Y=-25x²+200x+6000  in correct form.

 

TIP: If you graph the equation, you'll also find that the vertex of the equation is at (4,6400) meaning that the ideal ticket price for maximum takings is (12+x)= 12+4= $16 which give you takings of $6400