Question

A stadium has 52,00 seats. Seats sell for $35 in section A, $20 in section B, and $15 in section c. The number of seats in section A equals the total number of seats in both b and c. Suppose the stadium takes in $1,370,500 from each sold-out event.How many seats does each section hold??

Answer 1

Let the Total number of A seats be A

Let the Total number of B seats be B

Let the Total number of C seats be C

Given that the Total number of stadium seats = 52000

⇒ A + B + C = 52000

It is also mentioned that the number of seats in section A is equal to the total number of seats in both B and C

⇒ A = B + C

substituting the Value of A = B + C in A + B + C = 52000

⇒ A + A = 52000

⇒ 2A = 52000

⇒ A = 26000

⇒ The Number of Seats of A = 26000

⇒ The Number of Seats of Both B and C = 26000       (since A = B + C)

Given that Cost of Each seat of A = 35$

Cost of Each seat of B = 20$

Cost of Each seat of C = 15$

The Total Cost of all the seats = 1370500$

⇒ 35(A) + 20(B) + 15(C) = 1370500

dividing the entire equation with 5 we get :

⇒ 7A + 4B + 3C = 274100

but we know that number of seats of A = 26000

⇒ 7(26000) + 4B + 3C = 274100

⇒ 4B + 3C = 274100 - 182000

⇒ 4B + 3C = 92100

but we know that B + C = 26000 ⇒ C = 26000 - B

⇒ 4B + 3(26000 - B) = 92100

⇒ 4B + 78000 - 3B = 92100

⇒ B = 92100 - 78000

⇒ B = 14100

⇒ The Total Number of seats of B = 14100

As B + C = 26000

⇒ 14100 + C = 26000

⇒ C = 26000 - 14100

⇒ C = 11900

⇒ The Total number of seats of C = 11900

So the Stadium Holds a Total number of 52000 seats and In those 52000 seats A section holds 26000 seats and B section holds 14100 seats and C section holds 11900 seats.

Answer 2

Define x and y:

Let the number of seats in section B be x

Let the number of seats in section C be y

The number of seats in section A = x + y

Form equation 1:

Total number of seats = 52000 (Given)

x + y + (x + y) = 52000

x + y + x + y = 52000

2x + 2y = 52000

x + y = 26000

x = 26000 - y -------------------------- [ 1 ]

Form equation 2:

Total amount collected = $1,370,500

20x + 15y + 35(x + y) = 1,370,500

20x + 15y + 35x + 35y = 1,370,500

55x + 50y = 1,370,500

11x + 10y = 274,100 -------------------------- [ 2 ]

Put the two equations together:

x = 26000 - y            -------------------------- [ 1 ]

11x + 10y = 274,100   -------------------------- [ 2 ]

Find y:

Sub [ 1 ] into [ 2 ] :

11 (26000 - y) + 10y = 274,100

286000 - 11y + 10y = 274,100

y = 11,900    -------------------------- Sub into [ 1 ] to find x

Find x:

x = 26000 - y

x = 26000 = 11900

x = 14,100

Find the number of seats:

Section B = x = 14,100

Section C = y = 11,900

Section  A = x  + y = 14,100 + 11,900 = 26,000

Answer: There are 26,000 seats in Section A, 14,100 in section B and 11,900 in section C

Check:

Total number of seats = 26000 + 14100 + 11900 = 52,000

Total amount collected = 26000 x 35 + 14100 x 20 + 11900 x 15 = $1,370,500