A sports stadium has 10000 seats, divided into box seats, lower-deck seats, and upper-devk seats. Box seats sell for 10 dollars, lower-deck seats sell for 8 dollars, and upper-deck seats sell for 5 dollars.If all the seats are sold, the total revenue for a game is 70000 dollars.The stadium has 4 times as many upper* deckseats as box seats.How many lower-deck seats are in the stadium?

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isyllus isyllus · Answer 1 · 2020-09-02T02:36:33+02:00

Answer:

Number of box seats = 1000

Number of lower deck seats = 5000

Number of upper deck seats = 4000

Step-by-step explanation:

Let number of box seats = [tex]x[/tex]

Let number of lower deck seats = [tex]y[/tex]

Let number of upper deck seats = [tex]z[/tex]

As per question statement:

[tex]x+y+z=10000[/tex] ...... (1)

Cost for box seat = $10

Cost for [tex]x[/tex] box seats = 10[tex]x[/tex]

Cost for lower deck seat = $8

Cost for [tex]y[/tex] lower deck seats = 8[tex]y[/tex]

Cost for lower deck seat = $5

Cost for [tex]z[/tex] lower deck seats = 5[tex]z[/tex]

As per question statement:

[tex]10x+8y+5z=70000[/tex] ..... (2)

[tex]z = 4x[/tex] ..... (3)

Putting value of [tex]y[/tex] in (1) and (2):

[tex]x+y+4x=10000\\\Rightarrow 5x+y=10000[/tex] ....... (4)

[tex]10x+8 y+5\times 4x=70000\\\Rightarrow 30x+8y=70000 ..... (5)[/tex]

8 [tex]\times[/tex] (4) - (5):

[tex]10x =[/tex]10000

[tex]\Rightarrow x = 1000[/tex]

By (3):

[tex]z = 4000[/tex]

Now, by equation (1):

[tex]y[/tex] = 5000

Number of box seats = 1000

Number of lower deck seats = 5000

Number of upper deck seats = 4000