Since the weight is balanced on both sides, this implies that the moment at the fulcrum is zero. It simply means that, the summation of the product of the weight the distance on one side is the same to the other side of the teeterboard.

\(6(150) = Boy (4) +12 (Girl)\)

\(6(150) = Boy (8) +6 (Girl)\)

\(Boy = -3 (Girl) + 225\)

\(900 = 8(-3Girl+ 225) +6 (Girl)\)

\(-900+1800= 30 (Girl)\)

\(Girl = 50\)

\(Boy = -3 (50) + 225 = 75\)