Algebra word problem

Question

A vertical meter stick casts a shadow 1 7/8 ft. At the same time of day, a light post casts a shadow of 14 2/7 ft. How tall is the light post? Draw an image to represent the situation.

Answer 1

Let x be the height of the light post

Setting up the proportions using the given values:

15/8ft. / 100/7ft. = 1 m / xft.

15/8 / 100/7 = 3.28ft. / xft.

Solving by cross multiplication:

15/8 x = 100/7 * 3.28

x = 2627/105

x = 25 ft. (approx.)

Answer 2

P/(14 2/7) = 1/(1 7/8)

P/100/7 = 1/15/8

P = 100/7/15/8= (100/7)(8/15) = (20/7)(8/3) = 160/21

P= 160/21 = about 7.619

P = 7 13/21 meters= light Post height

14 2/7 is a little over 7 times 2 or 1 7/8

so the Post's height is a little over 7 times 1 metter

You might sketch two right similar triangles

together with the smaller inside the larger

so you can visually see that the sides of the base and height are proportional