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

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 = $x$

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)

$10x+8 y+5\times 4x=70000\\\Rightarrow 30x+8y=70000 ..... (5)$

8 $\times$ (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