.
a weight of 75 pounds is placed in a lever 15 feet from the fulcrum. how far from the fulcrum on the other
side must a weight of 90 pounds be placed in order to give equilibrium?
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According to the description, it is 1-st kind lever (1-st class lever).
For levers, see this Wikipedia article.
See also the lesson Using proportions to solve word problems in Physics in this site.
The condition for equilibrium for such levers is this equality
= 
,
where 
, 
are the forces applied and 
and 
are their armes.
In our case 75*15 = 90*x, which gives x = 
= 12.5 feet.
Answer. 12.5 feet.
