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A stadium has 50,000 seats. Seats sell for $42 in section A, $36 in section B, and $30 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 $1,888,800 from each sold out event. How many seats does each section hold?

Respuesta :

Katlyn93
A=B+C
2A=54000
A=27000 seats $30/seat=$810000
B+C=27000
24B+18C=571200
24B+18(27000-B)=571200
24B+486000-18B=571200
6B=85200
B=14200
C=12800
A=27000 seats, B=14200 seats, C=12800

Answer:

Section A has 25,000 seats.

Section B has 14,800 seats.

Section C has 10,200 seats.

Step-by-step explanation:

Let the seats in section A be = x

Let the seats in section B be = y

Let the seats in section C be = z

The equations forms as follows:

[tex]x+y+z=50000[/tex]           .....(1)

[tex]42x+36y+30z=1888800[/tex]        .......(2)

[tex]x=y+z[/tex] ......(3)

Substituting the value of x in (1) to get equation in two terms.

[tex]y+z+y+z=50000[/tex]

=> [tex]2y+2z=50000[/tex]

taking out 2 common, we get;

[tex]y+z=25000[/tex] .........(4)

And substituting the value of x in (2), we get

[tex]42(y+z)+36y+30z=1888800[/tex]

=> [tex]42y+42z+36y+30z=1888800[/tex]

=> [tex]78y+72z=1888800[/tex]

Taking out 2 common, we get;

[tex]39y+36z=944400[/tex]      ........(5)

Multiplying (4) by 39 and subtracting (5) from (4), we get

[tex]3z=30600[/tex]

We get z = 10200

And [tex]y+z=25000[/tex]

[tex]z=25000-10200=14800[/tex]

We get y = 14800

Also [tex]x=y+z[/tex]

[tex]x=14800+10200=25000[/tex]

We get x = 25000

Therefore,

Section A has 25,000 seats.

Section B has 14,800 seats.

Section C has 10,200 seats.