A stadium has 10,000 seats, divided into box seats, lower deck seats, and upper deck seats. Box seats sell for $10, lower deck seats sell for $8, and upper deck seats sell for $5. When all the seats for a game are sold, the total revenue is $70,000. The stadium has four times as many upper deck seats as box seats. Find the number of lower deck seats in the stadium using elimination.

the number of box seats    x  =  1000

the number of lower deck seats  y = 5000

the number of upper deck seats  z  = 4000

Step-by-step explanation:

Let´s call

"x"  the number of box seats    

"y" the number of lower deck seats  and

"z" the number of upper deck seats

Then

x + y + z = 10000    ( the total number of seats)    (1)

10*x  +  8*y  +  5*z  = 70000     (total revenue)      (2)

And  z = 4*x

Plugging  the value   z = 4*x  in equation (1)

x  +  y  +  4*x  =  10000

5*x + y = 10000   ⇒   y  =  10000 -   5*x

And plugging this value in equation (2)

10*x  +  8 * (10000 -  5*x ) + 20*x  =  70000

10*x  + 80000  - 40*x  + 20*x  =  70000

- 10*x   =  -10000

x  =  1000

Then

y  =  10000 -   5*x   ⇒   y = 10000 - 5 * ( 1000 )

y =  5000

And  z = 4*x      ⇒   z  = 4000