Solve.
-A basketball fieldhouse seats 15,000. Courtside seats sell for $8, endzone for $7, and balcony for $4. Total for a sell-out is $78,000. If half the courtside and balcony and all endzone seats are sold, the total is $46,000. How Many of each type are there?
A) 3200 courtside
1800 endzone
10,000 balcony

B) 3000 courtside
2000 endzone
10,000 balcony

C) 4000 courtside
3000 endzone
8000 balcony

Question

Solve.
-A basketball fieldhouse seats 15,000. Courtside seats sell for $8, endzone for $7, and balcony for $4. Total for a sell-out is $78,000. If half the courtside and balcony and all endzone seats are sold, the total is $46,000. How Many of each type are there? 
A) 3200 courtside
1800 endzone
10,000 balcony

B) 3000 courtside
2000 endzone
10,000 balcony

C) 4000 courtside
3000 endzone
8000 balcony

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. $8c + 7e + 4b = 78,000$ (total revenue for a sell-out)3. $4c + 7e + 2b = 46,000$ (revenue when half the courtside and balcony and all endzone seats are sold)Solving these equations simultaneously gives us $c = 3,000$, $e = 2,000$, and $b = 10,000$, which corresponds to option B.

Solve. -A Basketball Fieldhouse Seats 15,000. Courtside Seats Sell for $8