Question 447845: The total number of seats in a basketball sports arena is 12,000. The arena is divided into three sections, court sides, end zone and balcony, and there are twice as many balcony seats as court side seats. For the conference championship game, ticket price were $10.00 for court side, $8.00 for balcony and $7.00 for end-zone. If the arena was sold out for the game and the total receipts were $99,000 how many seats were court-side???.... thank you ^^
Found 3 solutions by mananth, stanbon, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! Courtside seats ----------x $10
balcony seats ------------2x$8
end zone seats ------------y $7
capacity 12000
Receipts =$99,000
..
x+2x+y = 12000
3x+y=12000
10x+8*2x+7y=99000
26x+7y= 99000
3x+y=12000 .............1
26x+7y= 99000 .............2
Eliminate y
multiply (1)by -7
Multiply (2) by 1
-21x-7y= -84000
26x+7y= 99000
Add the two equations
5x=15000
/5
x= 3,000
plug value of x in (1)
3x+y= 12000
9000+y=12000
y=12000 -9000
y=3000
Courtside seats ----------x ----3000
balcony seats ------------2x----6000
end zone seats ------------y----3000
CHECK
3 x + 1 y = 12000
9000 3000 = 12000
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! The total number of seats in a basketball sports arena is 12,000. The arena is divided into three sections, court sides, end zone and balcony, and there are twice as many balcony seats as court side seats. For the conference championship game, ticket price were $10.00 for court side, $8.00 for balcony and $7.00 for end-zone. If the arena was sold out for the game and the total receipts were $99,000 how many seats were court-side???....
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Seat Equation: c + e + b = 12000
Seat Equation:-2c+ 0 + b = 0
Value Equation:10c+7e+8b = 99,000
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I used a matrix function on a TI-84 to get:
court = 3000 seats
end zone = 3000 seats
balcony = 6000 seats
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Cheers,
Stan H.
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Answer by ikleyn(53560)  (Show Source):
You can put this solution on YOUR website! .
The total number of seats in a basketball sports arena is 12,000. The arena is divided into three sections,
court sides, end zone and balcony, and there are twice as many balcony seats as court side seats.
For the conference championship game, ticket price were $10.00 for court side, $8.00 for balcony
and $7.00 for end-zone. If the arena was sold out for the game and the total receipts were $99,000
how many seats were court-side?
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Two other solutions to this problem at this forum do introduce a system of three equations for
three unknown. Then they make many transformations and pronounce many words to solve
this system of equations, demonstrating great diligence and stupidity.
There is another, more elegant, straightforward and effective way to solve this problem
using only one equation and one unknown.
Let x be the number of the courtside seats.
Then the number of the balcony seats is 2x
and the number of the zone seats is (12000-x-2x) = (12000-3x).
Write the equation for the total money
10x + 8*(2x) + 7*(12000-3x) = 99000 dollars.
Simplify this equation and find x
10x + 16x + 84000 - 21x = 99000,
10x + 16x - 21x = 99000 - 84000,
5x = 15000,
x = 15000/5 = 3000.
So, the number of the court-side seats was 3000. ANSWER
Solved.
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