A basketball fieldhouse seats 15,000. Courtside seats sell for $10, endzone for $6, and balcony for $5. Total revenue for a sell-out is $92,000. If half the courtside and balcony and all the endzone seats are sold, the total
Revenue is $52,000. How many of each type of seat are there in the fieldhouse?
A) 3,200 courtside; 1,800 endzone; 10,000 balcony
B) 3,000 courtside; 2,000 endzone; 10,000 balcony
C) 4,000 courtside; 3,000 endzone; 8,000 balcony
D) 2,000 courtside; 5,000 endzone; 8,000 balcony

Question

Quizplus · Accepted Answer

Let the number of courtside, endzone, and balcony seats be $c$, $e$, and $b$ respectively. We have three equations based on the given information:1. $c + e + b = 15,000$ (total seats)2. $10c + 6e + 5b = 92,000$ (revenue from a sell-out)3. $10(\frac{1}{2}c) + 6e + 5(\frac{1}{2}b) = 52,000$ (revenue from half the courtside and balcony and all the endzone seats sold)Simplifying the third equation gives us $5c + 6e + 2.5b = 52,000$.Solving these equations simultaneously, we find that the only set of values that satisfies all conditions is $c = 3,000$, $e = 2,000$, and $b = 10,000$, which corresponds to option B.

A Basketball Fieldhouse Seats 15,000