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

Option DFunction used to determine the profit the theater group earns from selling "x" tickets is f(x) = 12.50x - 150Solution:Given that a theater group charges $12.50 per ticket for its opening play of the seasonAlso given that Production costs for the play are $150To find: function used to determine the profit the theater group earns from selling "x" ticketsSo "x" represents the number of tickets soldCost per ticket = $ 12.50[tex]\text { cost of "x" tickets }=" x " \times \text { cost per ticket }[/tex][tex]\text { cost of "x" tickets }= x \times 12.50=12.50x[/tex]Production costs = 150Then the profit the theater group earns from selling "x" tickets is:Profit earned from selling "x" tickets = cost of "x" tickets - production costLet f(x) denotes profit earned from selling "x" ticketsf(x) = 12.50x - 150Thus option D is correct