Solve.
-A basketball fieldhouse seats 15,000. Courtside seats sell for $10, endzone for $6, and balcony for $4. Total for a sell-out is $82,000. If half the courtside and balcony and all endzone seats are sold, the total is $47,000. How Many of each type are there?
A) 4000 courtside3000 endzone8000 balcony
B) 3000 courtside2000 endzone10,000 balcony
C) 3200 courtside1800 endzone10,000 balcony

Question

Quizplus · Accepted Answer

The problem can be solved using a system of equations based on the information given. Let x, y, and z represent the number of courtside, endzone, and balcony seats, respectively. We have:1. $x + y + z = 15,000$ (total seats)2. $10x + 6y + 4z = 82,000$ (total revenue for a sell-out)3. $\frac{1}{2}10x + 6y + \frac{1}{2}4z = 47,000$ (revenue when half the courtside and balcony and all endzone seats are sold)Solving this system of equations, we find that the correct distribution of seats that satisfies all conditions is 3000 courtside, 2000 endzone, and 10,000 balcony, which corresponds to choice B.

Solve. -A Basketball Fieldhouse Seats 15,000. Courtside Seats Sell for $10