77. Law of the Lever

 The figure shows a lever system, similar to a seesaw that you might find in a children's playground. For the system to balance, the product of the weight and its dis- tance from the fulcrum must be the same on each side; that is, 

\( w _ { 1 } x _ { 1 } = w _ { 2 } x _ { 2 }\) 

This equation is called the law of the lever and was first dis- covered by Archimedes (see page \( 787 \) ). 

A woman and her son are playing on a seesaw. The boy is at one end, \( 8 ft \) from the fulcrum. If the son weighs \( 100 lb \) and the mother weighs \( 125 lb \) , where should the woman sit so that the seesaw is balanced?