Answer:
Section A = 26,500 seats
Section B = 14,900 seats
Section C = 11,600 seats
Step-by-step explanation:
Total seats = 53,000
Total revenue = 1,997,400
Section A seat = $42
Section B seat = $36
Section C seat = $30
The number of seats in this in section A equals the total number of seats in section BNC
A = B + C
A + B + C = 53,000 (1)
42A + 36B + 30C = 1,997,400 (2)
Substitute A = B + C into (1)
A + B + C = 53,000
B + C + B + C = 53,000
2B + 2C = 53,000
2(B + C ) = 53,000
B + C = 53,000 / 2
= 26,500
B + C = 26,500 (3)
Substitute B + C = 26,500 into (2)
42A + 36B + 30C = 1,997,400
Recall,
A = B + C
42( 26,500) + 36B + 30C = 1,997,400
1,113,000 + 36B + 30C = 1,997,400
36B + 30C = 1,997,400 - 1,113,000
36B + 30C = 884,400. (4)
Multiply (3) by 30
B + C = 26,500 × 30
30B + 30C = 795,000 (5)
36B + 30C = 884,400 (4)
Subtract (5) from (4) to eliminate C
36B - 30B = 884,400 - 795,000
6B = 89,400
B = 89,400/6
= 14,900
B = 14,900
From (3)
B + C = 26,500
C = 26,500 - B
= 26,500 - 14,900
= 11,600
A = B + C
= 14,900 + 11,600
= 26,500
Section A = 26,500 seats
Section B = 14,900 seats
Section C = 11,600 seats
