Question 151000
A basketball fieldhouse seats 15,000. Courtside seats sell for $ 9, endzone for $7, and balcony for $4. The total revenue from a sell-out is $81,000. If half the courtside and balcony seats and all the endzone seats are sold, the total revenue is $47,500. How many of each type are there?
:
c = no. of courtside seats
e = no. of endzone seats
b = no. of balcony seats
:
Write a total seats equation:
c + e + b = 15000
:
Write an equation reflecting a sell-out:
9c + 7e + 4b = 81000
;
Write an equation for the statement:
"If half the courtside and balcony seats and all the endzone seats are sold, the total revenue is $47,500."
9(.5c) + 7e + 4(.5b) = 47500
which is:
4.5c + 7e + 2b = 47500
;
Using the above equation with the sell-out equation, eliminates e"
 9c + 7e + 4b = 81000
4.5c+ 7e + 2b = 47500
-----------------------subtraction eliminates e:
4.5c + 2b = 33500
:
Multiply the total seats equation by 7 and subtract from the sellout equation
9c + 7e + 4b =  81000
7c + 7e + 7b = 105000
----------------------- subtraction eliminates e
2c - 3b = -24000
;
Two equations, two unknowns, we should be able to handle this now
:
Multiply the 1st one by 3, and the 2nd one by 2; resulting in:
13.5c + 6b = 100500
 4c   - 6b = -48000
---------------------- addition eliminates b
17.5c = 52500
c = {{{52500/17.5}}}
c = 3000 courtside seats
:
Find b using; 4.5c + 2b = 33500
4.5(3000) + 2b = 33500
13500 + 2b = 33500
2b = 33500 - 13500
2b = 20000
b = {{{20000/2}}}
b = 10000 balcony seats
;
I'll let you find the number of endzone seats