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# The figure above shows a cross section of a grandstand that seats 1000

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Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132619 [0], given: 12326

The figure above shows a cross section of a grandstand that seats 1000 [#permalink]

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05 Sep 2017, 23:41
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25% (medium)

Question Stats:

83% (00:48) correct 17% (00:50) wrong based on 26 sessions

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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

[Reveal] Spoiler:
Attachment:

2017-09-06_1034.png [ 9.88 KiB | Viewed 412 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 132619 [0], given: 12326

Director
Joined: 22 May 2016
Posts: 979

Kudos [?]: 337 [0], given: 591

The figure above shows a cross section of a grandstand that seats 1000 [#permalink]

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06 Sep 2017, 12:43
Bunuel wrote:

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

[Reveal] Spoiler:
Attachment:
2017-09-06_1034.png

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

*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.

Kudos [?]: 337 [0], given: 591

The figure above shows a cross section of a grandstand that seats 1000   [#permalink] 06 Sep 2017, 12:43
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