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

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

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.

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