Question

A theater group charges $12.50 per ticket for its opening play of the season. Production costs for the play are $150. Which function could be used to determine the profit the theater group earns from selling x tickets?
A)
f(x) = 12.50x


B)
f(x) = 12.50x + 150


C)
f(x) = 150x −12,50


D)
f(x) = 12.50x − 150

Answer 1

Option D

Function used to determine the profit the theater group earns from selling "x" tickets is f(x) = 12.50x - 150

Solution:

Given that a theater group charges $12.50 per ticket for its opening play of the season

Also given that Production costs for the play are $150

To find: function used to determine the profit the theater group earns from selling "x" tickets

So "x" represents the number of tickets sold

Cost per ticket = $ 12.50

$\text { cost of "x" tickets }=" x " \times \text { cost per ticket }$

$\text { cost of "x" tickets }= x \times 12.50=12.50x$

Production costs = 150

Then the profit the theater group earns from selling "x" tickets is:

Profit earned from selling "x" tickets = cost of "x" tickets - production cost

Let f(x) denotes profit earned from selling "x" tickets

f(x) = 12.50x - 150

Thus option D is correct