How of each seat are there?

Question

a basketball field house seats 15,000. court side seats sell for &=$8, end zone for $6, and balcony for $4. a full house earns $76000 in ticket revenue. if half the court side and balcony sears and all the end zone seats are sold, the total ticket revenue is $44,000. how many of each type of seats are there

Answer 1

let x=# of courtside seats

let y=# of end zone seats

let z=# of balcony seats

set up three equations with three unknowns

 

15,000=x+y+z

76,000=8x+6y+4z

44,000=(0.5x)(8)+6y+(0.5z)(4)

multiply third equation by 2

88,000=8x+12y+4z

subtract second equation from the new third equation

88,000=8x+12y+4z

-

76,000=8x+6y+4z

12,000=6y

12,000/6=y

2,000=y

substitute into the first equation

15,000=x+2,000+z

15,000-2,000=x+z

13,000=x+z

use the second equation with y=2,000

76,000=8x+12,000+4z

76,000-12,000=8x+4z

64,000=8x+4z

divide this equation by 4

16,000=2x+z

use this equation with 13,000=x+z

16,000=2x+z

13,000=x+z

subtract these equations

3,000=x

use equation one

15,000=3,000+2,000+z

15,000=5,000+z

15,000-5,000=z

10,000=z

3,000 courtside seats

2,000 end zone seats

10,000 balcony seats

8(3,000)+6(2,000)+4(10,000)=24,000+12,000+40,000=$76,000