Answer:
Section A = 27,500 seats
Section B = 14,800 seats
Section C = 12,700 seats
Step-by-step explanation:
Section A = $42
Section B = $24
Section C = $18
Revenue = $1,738,800
Total number of seats = 55,000
The number of seats in Section A equals the total number of seats in Sections B and C
A = B + C
A + B + C = 55,000
42A + 24B + 18C = $1,738,800
Substitute A = B + C into the equations
B + C + B + C = 55,000
42(B + C) + 24B + 18C = $1,738,800
2B + 2C = 55,000
42B + 42C + 24B + 18C = 1,738,800
2B + 2C = 55,000
66B + 60C = 1,738,800
Multiply (1) by 30
60B + 60C = 1,650,000. (1)
66B + 60C = 1,738,800. (2)
Subtract (1) from (2)
66B - 60B = 1,738,800 - 1,650,000
6B = 88,800
B = 88,800/6
= 14,800
B = 14,800
Substitute the value of B into
2B + 2C = 55,000
2(14,800) + 2C = 55,000
29,600 + 2C = 55,000
2C = 55,000 - 29,600
2C = 25,400
C = 25,400/2
= 12,700
C = 12,700
Substitute the values of B and 6 into
A + B + C = 55,000
A + 14,800 + 12,700 = 55,000
A + 27,500 = 55,000
A = 55,000 - 27,500
= 27,500
A = 27,500
Section A = 27,500 seats
Section B = 14,800 seats
Section C = 12,700 seats
