When a seesaw is balanced, each person's weight varies inversely with the distance from the center support. If a person who weigh 90lbs sits at one end of a 12ft seesaw, how far from the support must a 120lb person sit in order to balance the seesaw?

Saying that the person's weight vairies inversely with the distance to the support is like saying that the person's weight (call it W) times the distance (L) is a constant (C). In other words:


W \times L = C


For two people to be balanced, each person's weight times distance must be equal:


W_1 \times L_1 = C = W_2 \times L_2


Here you have the weight and distance for one person, and the weight for the second person, so now you can solve for the distance of the second person.