Solve the problem.
-A theater charges $50 per ticket for seats in section A, $40 per ticket for seats in section B, and $20 per ticket for seats in section C. For one play, 9,500 tickets were sold for a total of $335,000 in
Revenue. If 500 more tickets in section B were sold than the other two sections combined, how many
Tickets in each section were sold?
A) 3,000 tickets in section A, 5,000 tickets in section B, and 1,500 tickets in section C were sold.
B) 3,000 tickets in section A, 3,500 tickets in section B, and 1,500 tickets in section C were sold.
C) 1,500 tickets in section A, 3,500 tickets in section B, and 3,000 tickets in section C were sold.
D) 1,500 tickets in section A, 5,000 tickets in section B, and 3,000 tickets in section C were sold.

Question

Quizplus · Accepted Answer

Let the number of tickets sold in sections A, B, and C be A, B, and C respectively. We have three equations based on the given information:1. $A + B + C = 9500$ (total tickets sold)2. $50A + 40B + 20C = 335,000$ (total revenue)3. $B = A + C + 500$ (500 more tickets in section B than A and C combined)Substituting $B = A + C + 500$ into the first equation gives $A + (A + C + 500) + C = 9500$, simplifying to $2A + 2C = 9000$, or $A + C = 4500$.Substituting $B = A + C + 500$ into the second equation gives $50A + 40(A + C + 500) + 20C = 335,000$. Simplifying and using $A + C = 4500$, we can solve for A, B, and C.Solving these equations, we find that $A = 1500$, $B = 5000$, and $C = 3000$, which matches option D.

Solve the Problem. -A Theater Charges $50 Per Ticket for Seats in Section