math help story problem

Question

A stadium has 47,000 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 ​$1,216,800 from each​ sold-out event. How many seats does each section​ hold?

Answer 1

a=b+c

a+b+c=47,000

30a + 24b + 18c =1,216,800

3 equations, 3 variables, solve by substitution elimination or matrix algebra

30(b+c) +24b+ 18c 1216800

54b + 48c = 1216800

27b +24c = 608400

b+c +b+c = 47000

2b +2c = 47000

b +c = 23500

24b +24c = 24(23500)

3b = 608,400 -24(23500)

b = 202,800 - 8(23500)

b = 202,800-188,000

b= 14,800 seats sold in the B section

c= 23,500-14,800= 8,700 seats sold in C section

a = b+c = 14,800+8,700 = 23,500 seats sold in A section

23,500+14,800+8,700 = 47,000 = seat capacity

30(23,500) + 24(14,800) + 18(8,700) = $1,216,800 = total revenue