Question

A stadium has 45,000 seats. Seats sell for ​$30 in Section​ A, ​$24 in Section​ B, and ​$18 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in ​$1,168,800 from each​ sold-out event. How many seats does each section​ hold?

Answer 1

a + b + c = 45,000
30a + 24b + 18c = 1,168,800 reduces to 5a + 4b + 3c = 194,800
a = b + c

b + c + b + c = 45,000
2b + 2c = 45,000
b + c = 22500 <=== this is A
c = 22500 - b

5a + 4b + 3c = 194,800
5(22500) + 4b + 3(22500 - b) = 194,800
112500 + 4b + 67500 - 3b = 194,800
b + 180,000 = 194,800
b = 194,800 - 180,000
b = 14,800 <===here is b

a = b + c
22500 = 14800 + c
22500 - 14800 = c
7700 = c <== here is c

so....A = 22,500, B = 14,800, and C = 7,700