1. use the law of levers to solve the problem, x1y1=x2y2.
a 27 kg weight is placed 10 feet from the fulcrum on one side, and a 30 kg weight is placed x feet from the fulcrum on the other side. what is x?
a. 9
b. 15
c. 12
d. 8
2. which equation is the inverse variation relationship for the following quantities? y =-12 when x = 5
a. y = -2.4x
b. y/x = -2.4
c. xy = -60

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