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05 Sep 2017, 23:41
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D
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Difficulty:
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Question Stats:
88% (01:03) correct
12%
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wrong
based on 82
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The figure above shows a cross section of a grandstand that seats 1000 people per 2 yards of slant height. What is the total number of seats in the grandstand?
(A) 25,000
(B) 35,000
(C) 40,000
(D) 50,000
(E) 100,000
Attachment:
2017-09-06_1034.png [ 9.88 KiB | Viewed 3268 times ]
06 Sep 2017, 12:43
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Bunuel
I think Answer D. It is a little strange to be calculating what seems like a measure of area (into which 3-D seats fit), with one dimension (slant height).*
The figure is a 3x-4x-5x right triangle, where slant height is the hypotenuse. The multiplier is 20.
3 * 20 = 60
4 * 20 = 80
5 * 20 = 100
So the slant height of the grandstand is 100 yards
The grandstand "seats 1000 people per 2 yards of slant height." Set up a proportion with two ratios. Total number of seats in the grandstand?
\(\frac{1000 people}{2 yds} = \frac{X people}{100 yds}\)
Because denominator of 2 is multiplied by 50 (to yield 100), multiply numerator of 1,000 by 50 = 50,000. Or cross multiply.
2x = (1000)(100)
2x = 100,000
x = 50,000
Answer D
*Sometimes I get stuck on odd details. Would someone please explain how that which seems linear (slant height) can account for that which seems two-dimensional (area into which seats fit)? I would appreciate it.
27 Apr 2018, 06:50
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Answer is D.
Here, Slant height (Hypotenuse) b^2= 60^2+80^2 (According to The Pythagoras Theorem)
b^2=10000
b=100
Given that, a cross section of a grandstand that seats 1000 people per 2 yards of slant height
So, 100/2=50 *1000
= 50,000 (Answer D)
Here, Slant height (Hypotenuse) b^2= 60^2+80^2 (According to The Pythagoras Theorem)
b^2=10000
b=100
Given that, a cross section of a grandstand that seats 1000 people per 2 yards of slant height
So, 100/2=50 *1000
= 50,000 (Answer D)
