Question 1124210: A stadium has 54000 seats. Seats sell for $30 in Section A, $24 in Section B, and $18 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1382400 from each sold-out event. How many seats does each section hold?
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website! "The number of seats in Section A equals the total number of seats in Sections B and C."
This tells us that the number of seats in Section A is exactly half of the 54,000 seats the stadium holds...27,000 seats...with the other two sections combining for the remaining 27,000 seats. Therefore, with regard to the number of seats in Sections B and C, we know:
B + C = 27000
"Seats sell for $30 in Section A, $24 in Section B, and $18 in Section C."
"Suppose the stadium takes in $1,382,400 from each sold-out event."
We already know that there are 27,000 seats in Section A that sell for $30. We also know how much the seats in the other sections sell for, as well as the total "take" from a sell-out. But, we still do not know how many seats are in Section B and Section C. Therefore, with regard to the money, we know:
30(27000) + 24B + 18C = 1382400
Simplify this:
810000 + 24B + 18C = 1382400
24B + 18C = 572400
We are left with two equations:
B + C = 27000
24B + 18C = 572400
Multiply the first equation by -18:
-18B - 18C = -486000
24B + 18C = 572400
Add the two equations together:
6B = 86400
Solve for B:
B = 14400
This means there are 14,400 seats in Section B.
Looking at the equation B + C = 27000, if you plug in 14400 for B, this would mean C = 12600. So, Section C has 12,600 seats.
In summary:
Section A = 27,000 seats
Section B = 14,400 seats
Section C = 12,600 seats
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Double-check:
Section A: 27,000 seats @ $30 each = $810,000
Section B: 14,400 seats @ $24 each = $345,600
Section C: 12,600 seats @ $18 each = $226,800
$810,000 + $345,600 + $226,800 = $1,382,400
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