A588 mother sits on one side of a seesaw, 2.20m away from the pivot. one of her two children sits 2.00m from the pivot on the other side of the seesaw. if the force of gravity on her is 256n, where must the other child sit to balance the seesaw if the force of gravity on him is 412 n ?

Using momentum balance:

The 588 N mother is on the other side of the seesaw, 2.20m away from the pivot

F1 = 588 N
x1 = 2.20 m

Two of her children sat on the other side:

F2 = 256 N
x2 = 2.00 m

F3 = 412 N
x3 = unknown

F1x1 = F2x2 + F3x3

Solve for x3:

588 * 2.2 = 256 * 2 + 412 * x3

x3 =  1.90 meters away from pivot