Question

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?

Answer 1

Number of box seats = 1000

Number of lower deck seats = 5000

Number of upper deck seats = 4000

Explanation:

Let number of box seats =
`x`

Let number of lower deck seats =
`y`

Let number of upper deck seats =
`z`

As per question statement:

`x+y+z=10000` ...... (1)

Cost for box seat = $10

Cost for
`x` box seats = 10
`x`

Cost for lower deck seat = $8

Cost for
`y` lower deck seats = 8
`y`

Cost for lower deck seat = $5

Cost for
`z` lower deck seats = 5
`z`

As per question statement:

`10x+8y+5z=70000` ..... (2)

`z = 4x` ..... (3)

Putting value of
`y` in (1) and (2):

`x+y+4x=10000\\\Rightarrow 5x+y=10000` ....... (4)

`10x+8 y+5* 4x=70000\\\Rightarrow 30x+8y=70000 ..... (5)`

8
`*` (4) - (5):

`10x =`10000

`\Rightarrow x = 1000`

By (3):

`z = 4000`

Now, by equation (1):

`y` = 5000

Number of box seats = 1000

Number of lower deck seats = 5000

Number of upper deck seats = 4000