Andrew M. answered • 02/20/17
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
Let c = # courtside seats
Let b = #balcony seats
Let e = # endzone seats
The fieldhouse seats 15,000:
c + b + e = 15000 {eqn 1)
From a complete sell out the revenue is 89,000:
9c + 5b + 6e = 89,000 {eqn 2)
half the courtside and balcony seats and all the endzone
seats are sold, the total revenue is $50,500:
9(.5c) + 5(.5b) + 6e = 50,500 {eqn 3}
4.5c + 2.5b + 6e = 50,500
45c + 25b + 60e = 505,000 10(eqn 3)
We have a system of 3 equations with 3 unknowns:
c + b + e = 15000 {eqn 1)
9c + 5b + 6e = 89,000 {eqn 2)
45c + 25b + 60e = 505,000 {eqn 3}
Let's reduce this to 2 equations with 2 unknowns
by eliminating the b variable:
multiply eqn 1 by -5 and add to eqn 2
-5c - 5b - 5e = -75000
9c + 5b + 6e = 89,000
----------------------------
4c + e = 14,000
Now eliminate the b variable from eqn 1 and eqn 3:
Multiply eqn 1 by -25 and add to eqn 3
-25c - 25b - 25 e = -375,000
45c + 25b + 60e = 505,000
--------------------------------------
20c + 35e = 130,000
Now we have 2 equations with 2 unknowns:
4c + e = 14,000
20c + 35e = 130,000
Multiply the top equation by -5 and add to bottom:
-20c - 5e = - 70,000
20c + 35e = 130,000
-----------------------------
30e = 60,000
e = 2,000 endzone seats
4c + e = 14000
4c + 2000 = 14000
4c = 12000
c = 3,000 courtside seats
c + b + e = 15000
3000 + b + 2000 = 15000
b + 5000 = 15000
b = 10,000 balcony seats
ChecK: 9c + 5b + 6e = 89,000
Andrew M.
Okay, you're wrong:
eqn 2:
4.5c + 2.5b + 9e = 50,500
4.5(3250) + 2.5(10,750) + 9000 = 50,500
14625 + 26875 + 9000 = 50,500
50,500 = 50,500
eqn 3
9c + 5b + 6e = 89,000
9(3250) + 5(10,750) + 6(1000) = 89,000
89,000 = 89,000
My answer is correct for the total number of each type of seat
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02/20/17
Andrew M.
George,
In equation 3 I accidentally replaced the cost of
endzone seats with $9 instead of $6. Thank you.
But your answer is still incorrect ....
There are 3,000 courtside, 2,000 endzone, and
10,000 balcony seats.
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02/20/17
Andrew M.
c + b + e = 15,000
3,000 + 10,000 + 2,000 = 15000 √
9c + 5b + 6e = 89,000
9(3,000)+5(10,000)+6(2,000) = 89000
27000 + 50000 + 12000 = 89000
89000 = 89000 √
4.5c + 2.5b + 6e = 50,500
4.5(3000)+2.5(10,000)+6(2,000) = 50500
13500+25000+12000 = 50500
50500 = 50500 √
3,000 + 10,000 + 2,000 = 15000 √
9c + 5b + 6e = 89,000
9(3,000)+5(10,000)+6(2,000) = 89000
27000 + 50000 + 12000 = 89000
89000 = 89000 √
4.5c + 2.5b + 6e = 50,500
4.5(3000)+2.5(10,000)+6(2,000) = 50500
13500+25000+12000 = 50500
50500 = 50500 √
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02/20/17
George S.
yeah, forget to add one more 0, thanks
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02/20/17
Andrew M.
No problem. It's too easy to drop a zero or a sign.
And, again, thanks for looking at my answer.
Sucks to work out that whole thing with a
wrong coefficient in the original equation. lol.
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02/20/17
George S.
02/20/17