Difference between revisions of "1995 AHSME Problems/Problem 16"
(New page: ==Problem== Anita attends a baseball game in Atlanta and estimates that there are 50,000 fans in attendance. Bob attends a baseball game in Boston and estimates that there are 60,000 fans ...) |
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i. The actual attendance in Atlanta is within <math>10 \%</math> of Anita's estimate. | i. The actual attendance in Atlanta is within <math>10 \%</math> of Anita's estimate. | ||
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ii. Bob's estimate is within <math>10 \%</math> of the actual attendance in Boston. | ii. Bob's estimate is within <math>10 \%</math> of the actual attendance in Boston. | ||
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==Solution== | ==Solution== | ||
− | Since the number of people at the game in Boston is certainly more than the number of fans in Atlanta, we need to compute the maximum of Bob's game minus the minimum of Anita's game. | + | Since the number of people at the game in Boston is certainly more than the number of fans in Atlanta, we need to compute the maximum of Bob's game minus the minimum of Anita's game. Note however that there is a slight different between conditions (i) and (ii); the attendence is ''within'' <math>\pm 10 \%</math> from Anita's estimate of <math>50,000</math>, but Bob's estimate is ''within'' <math>\pm 10 \%</math> of the actual attendance, or <math>0.9x \le 60000 \le 1.1x \Longrightarrow x \le \frac{60000}{0.9}</math>. |
− | <math>60000 | + | The answer is <math>\frac{60000}{0.9} - 50000 \times 0.9 \approx 22000 \Longrightarrow \mathrm{(E)}</math>. |
==See also== | ==See also== | ||
+ | {{AHSME box|year=1995|num-b=15|num-a=17}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 12:59, 5 July 2013
Problem
Anita attends a baseball game in Atlanta and estimates that there are 50,000 fans in attendance. Bob attends a baseball game in Boston and estimates that there are 60,000 fans in attendance. A league official who knows the actual numbers attending the two games note that:
i. The actual attendance in Atlanta is within of Anita's estimate.
ii. Bob's estimate is within of the actual attendance in Boston.
To the nearest 1,000, the largest possible difference between the numbers attending the two games is
Solution
Since the number of people at the game in Boston is certainly more than the number of fans in Atlanta, we need to compute the maximum of Bob's game minus the minimum of Anita's game. Note however that there is a slight different between conditions (i) and (ii); the attendence is within from Anita's estimate of , but Bob's estimate is within of the actual attendance, or .
The answer is .
See also
1995 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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