Before a championship soccer match, Tara and Emek helped stadium staff decide how many seating sections to prepare. The stadium held 30,000 spectators, and advance records showed that 84 percent of the seats had been sold. Tara calculated that 25,200 tickets were sold. Staff also expected 12 percent of ticket holders not to attend. Emek warned that they should not simply subtract 12 percentage points from 84 percent because the 12 percent applied only to sold tickets. Instead, they expected 88 percent of the 25,200 ticket holders to arrive, giving an estimated attendance of 22,176. Each seating section held 1,200 people. Eighteen sections would provide only 21,600 seats, so Tara and Emek recommended opening 19 sections, providing 22,800 seats. This left 624 seats beyond the expected attendance. Stadium staff followed their plan, and when the gates opened, spectators were seated efficiently without preparing far more space than necessary.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
First account for the percentage of seats sold. Then remember that 88 percent of those ticket holders are expected to attend.
Which expression correctly represents the expected attendance using the stadium capacity, the 84 percent ticket-sale rate, and the expected 12 percent no-show rate?
30000(0.84 - 0.12)30000(0.84)(0.12)30000(0.84)(0.88)30000(0.88)(0.88)
Correct. The 84 percent applies to all seats, and then the 88 percent attendance rate applies to the sold tickets.
Not quite. The 12 percent no-show rate applies to ticket holders, not directly to the full stadium capacity.
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Hint
Convert 12 percent to a decimal and multiply it by the number of sold tickets.
Using the 25,200 sold tickets from the story, how many ticket holders are expected not to attend if the no-show rate is 12 percent?
Correct. The expected number of no-shows is 3,024.
Check that the 12 percent is applied to the 25,200 sold tickets rather than to the full stadium capacity.
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Hint
The incorrect method gives 84 percent - 12 percent = 72 percent of the 30,000-seat capacity. Compare that result with 22,176.
Suppose stadium staff incorrectly estimate attendance by subtracting the 12 percent no-show rate directly from the 84 percent ticket-sale rate. How does their estimate compare with the correct expected attendance of 22,176?
Their estimate is 576 lower than the correct attendance.Their estimate is 576 higher than the correct attendance.Their estimate is 3,024 lower than the correct attendance.Their estimate is exactly the same as the correct attendance.
Correct. The incorrect method gives 21,600, which is 576 fewer than the correct estimate of 22,176.
Not quite. First find 72 percent of 30,000, then compare it with the correct expected attendance.
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Şampiyona Kalabalığını Planlamak
TR
ARC_G11_FRD_02_STORY_02
Şampiyona Kalabalığını Planlamak
Planning for the Championship Crowd
EN
ARC_G11_FRD_02_STORY_02
Planning for the Championship Crowd