Use a Graphing Calculator and the Method of Matrix Inverses $\$ 10$

Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary.
-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) 4,000 courtside; 3,000 endzone; 8,000 balcony
B) 2,000 courtside; 5,000 endzone; 8,000 balcony
C) 3,000 courtside; 2,000 endzone; 10,000 balcony
D) 3,200 courtside; 1,800 endzone; 10,000 balcony