Question

Tasha has mass 20 kg and wants to use a 4.0-m board of mass 10 kg as a seesaw. her friends are busy, so tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board. how far is she from the support point?

Answer 1

The 4 m board's center of mass is 2 m so the pivot point is somewhere between Tasha and 2 m (if you draw a picture it's going to make this clearer)

 The mass of Tasha * her distance from the pivot point = the board's mass * distance from the pivot point. 
 Let d1 be the distance Tasha is from the pivot point. The board's center of mass from the pivot point is 2 m - d1 
 20 kg * d1 = 10 kg * (2m - d1) 
 Solve for d1, you should get 2/3 of a m for the distance Tasha is from the pivot or support point. The center of mass for the board is 1 1/3 m from the support point.