A stadium has 55,000 seats. Seats sell for $42 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 $1,738,800 from each sold-out event. How many seats does each section hold?

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

Answer:

Section A has 27,500 seats

Section B has 14,800‬ seats

Section C has 12,700‬ seats

Step-by-step explanation:

To solve this, we will have equations:

let x = seats at section A

  y= seats at section B

 Z = seats at section C

we will get the following equation:

So from the question, x = y + z ..........(1)

                     x + y + z = 55,000 .........(2)

                  42x + 24y + 18z = 1,738,800 .... (3)

input equation (1) into (2)

 y + z + y + z = 55,000

2y + 2z = 55,000...... (4)

so for exuation (3), input equation (1) into (3):

42x + 24y + 18z = 1,738,800

42(y + z) + 24y + 18z = 1,738,800

42y + 42z + 24y + 18z = 1,738,800

collect like terms:

66y + 60z = 1,738,800 ..... (5)

multiply equation (4) by -30. -30 is chosen to remove z from the equation so we could get what y is

-60y - 60z = - 1,650,000‬ ...... (6)

add equation (5) and (6)

6y + 0 = 88,800‬

y = 14,800‬ seats

Input the value of y into equation (4) to find z

2y + 2z = 55,000

2(14,800) + 2z = 55,000

29,600 + 2z = 55,000

2z = 25,400‬

z = 12,700‬ seats

To find the number of seats in section A we use equation (2)

x + y + z = 55,000

x +14,800 + 12,700 = 55,000

x + 27,500 = 55,000

x = 27,500 seats

To verify our answer to see if the number of seats in Section A equals the total number of seats in Sections B and C.

total number of seats in Sections B and C = 14,800 + 12,700 = 27,500

so number of seats in section A = B + C

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