Question

A cactus casts a shadow that is 15 ft long. A gate nearby casts a shadow that is 5 ft long at the same moment. If the height of a gate is 3ft long, what is the height of the cactus?

Step-by-step explanation:
There is more than 1 way to do this problem, but all of them involve proportions. It’s a good idea to learn how a proportion works: it’s one of the key tools of the sciences.
Let the height of the Cactus = x
Ratio Cactus    =     Ratio Gate.
x/15               =            3/5
Notice that both ratios are set up as height / shadow. If you do this all the time (keep the ratio the same), you will never make a mistake on proportions.
x/15 = 3/5                     Cross Multiply
5x = 15 * 3                    Combine.
5x = 45                         Divide by 5
5x/5 = 45/5
x = 9
The height of the cactus has to be less than the length of its shadow, which it is.