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Question

The estimated number of tickets that will be sold by a theme park during a weekend is given by the function n = 6000 / (5p - k), where p is the price of a ticket in dollars and k is a constant. At $5 a ticket the park estimates to sell 400 tickets. How many tickets will be sold at $4 a ticket?
A. 500
B. 450
C. 600
D. 625
E. 800

Correct Answer : Choice C

The estimated number of tickets that will be sold is given by the function n = 6000 / (5p - k).

p is the price per ticket.

When = $5, the theme park sells 400 tickets. i.e., n = 400.

Substituting these value in the function, we get 400 = 6000 / (5*5 - k)
or 400 = 6000 / (25 - k)
or 400(25 - k) = 6000

Solving for k, we get k = 10.

So, the function can be written in terms of n and p as n = 6000 / (5p - 10).

When p = 4, we get n = 6000 / (5*4 - 10) = 6000 / 10 = 600 tickets.