Question

The stadium has 53,000 seats seats sell for $42 in section 8 $36 in section B $30 in section C the number of seats in this in section 8 equals the total number of seats in section BNC supposed to stadium takes in 1,997,400 from each sold out I meant how many seats does each section hold

Answer 1

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