Inverse proportions math word problem

Question

Sam takes a picture of himself standing 3.0 meters from his camera and finds the size of his
image to be 6.0 cm. In another photograph of himself he finds his image to be 2 cm tall. What is his
distance from the same camera in the second picture? Image size is inversely proportional to the
object distance.

Answer 1

In my opinion, Samuel, your textbook has poorly stated this problem. If you set it up the way they implied then you will indeed get 1 meter as your answer; however, when you think about it, for the image to get smaller Sam would have to be further from his camera, not closer to it.

So set the 2 cm side( the vertical side) 300 cm( 3 meters) from the camera. Now how far from the camera does the 6 cm image have to be so the angles remain the same( respective sides are proportional)?
Now set up your proportions as 300 / 2 = X / 6. Solving for X we get 1800 / 2 = 900 cm, which is 9 meters as your textbook has.

Answer 2

3m : 6cm=X : 2cm

X=1m