Question

The owner of a baseball stadium found that he sells an average of 586 tickets to each game when he charges an average of $59 per ticket. In addition, he found that with every $6 increase in ticket price, the average number of tickets sold decreases by an average of 4. Which of the following functions describes the baseball stadium's profit in terms of x, the number of $6 increases over $59?

Answer 1

Given that the owner of a baseball stadium found that he sells an average of 586 tickets to each game when he charges an average of $59 per ticket.

So number of tickets = 586

Profit on 1 ticket = $59

Say price is increased once then new cost of ticket = 59+6

Say price is increased twice then new cost of ticket = 59+6*2

Say price is increased thrice then new cost of ticket = 59+6*3

In the same pattern

Say price is increased x-times then new cost of ticket = 59+6*x

In same pattern number of tickets sold will decrease by multiple of 4

Hence number of tickets sold  when cost is increased x-times = 586-4*x

Then profit when cost is increased x-times = (586-4*x) (59+6*x)

Let P(x) represents profit when price is increased x-times then the required function will be:

P(x)= (586-4x)(59+6x)

Hence final answer will be choice matching with P(x)= (586-4x)(59+6x)