1) Never heard of someone referring to the Law of Levers before, must be showing my age. A system as you describe is at equilibrium when the net torque is equal to zero. Since torque is Fr=mgr so for this system we have a sum of:
27g*10+30g*x=0 The sum must be zero to be at equilibrium, dividing both sides by g you have:
270+30x=0
270=-30x
x=-9
The negative just indicates that the magnitude of 9 is on the opposite side of the fulcrum, so x=9ft in magnitude.
2) Inverse variation is of the form y=k/x, in this case we are given a point so we can solve for the constant, k, of variation...
y=k/x, and we are given y=-12 when x=5 so
-12=k/5
k=-60 so the equation is:
y=-60/x which can be expressed as
xy=-60