SOLUTION: write a function that models each variation. x=3 and y=12 when z=2. z varies directly with y and inversely with x.

The formula for all variation problems is: 


                     k*{DIRECTLY OR JOINTLY VARIABLE(s) (or 1 if none)}
VARYING VARIABLE = -----------------------------------------------------
                         {INVERSELY VARIABLE(s) (or 1 if none)}

The varying variable is z, which goes on the left side.
The directly variable is y, which goes in the numerator on the right.
The inversely variable is x, which goes in the denominator on the right.

                      
               
                      

All we need do is find constant k and rewrite this 
substituting what we get for constant k.

To get k, we substitute the data given, x=3, y=12, z=2.

              

              

              

              

              

Now we rewrite  

               

substituting  for constant 
                      
               

Simplify by multiplying top and bottom on the right 
side by 2:

               

               

               

Edwin