x varies directly as y and inversely as the square of z. If x=10 when y=8 and
z=2, find x when y=12 and z=3.

Formula:
                       
                       "directly" variable (or product of "jointly" variables)
                         (if no directly or jointly variables, write 1 here)
"Varying" quantity = k·---------------------------------------------------------
                      "inversely" variable (or product of "inversely variables")
                        (If no inversely variable(s), write 1 here)

The "varying" quantity is x.
There is one "directly" variable, y
There is one "inversely" variable, z²

Substituting
                      y
               x = k·----
                      z²

Substituting the complete set of data, 
where ALL the variables are given:

x=10, y=8, z=2


                      8
              10 = k·----
                      2²

Solve for k

                      8
              10 = k·---
                      4    
                
                      
              10 = k·2

              10 = 2k

                5 = k

Now substitute k = 5 into:

                      y
               x = k·----
                      z²

which gives:

                      y
               x = 5·----
                      z²
                      

Now substitute the second set of data,
and solve for the missing letter x

Substitute y=12 and z=3 into

                      y
               x = 5·----
                      z²

                      12
               x = 5·----
                      3²

                      12
               x = 5·----
                       9

3 divides into 9 to give 3 and into 12 to give 4:

                       4
                      12
               x = 5·----
                       9
                       3
                           

                      4
               x = 5·---
                      3
                

                    20
               x = ----
                     3

               x = 6

Edwin