Write a System of Equations and Use the Inverse of the Coefficient

Write a system of equations and use the inverse of the coefficient matrix to solve the system.
-A basketball fieldhouse seats 15,000 . Courtside seats sell for $\$ 10$ , endzone for $\$ 7$ , and balcony for $\$ 4$ . Total for a sell-out is $\$ 84,000$ . If half the courtside and balcony and all endzone seats are sold, the total is $\$ 49,000$ . How many of each type are there?

A) 3200 courtside
1800 endzone
10,000 balcony
B) 3000 courtside
5000 endzone
7000 balcony
C) 3000 courtside
2000 endzone
10,000 balcony
D) 4000 courtside
3000 endzone
8000 balcony