FORMULA:

                          product of "directly" or "jointly" variables
"Varies as" variable = k* --------------------------------------------
                              product of "inversely" variables

The "varies as" variable is z, so write:


                   z = k*-----

The "directly variables" are x and y, so write them on the top:

                          xy
                   z = k*----- 


There is just one "inversely variable", w, so write it on the bottom:


                          xy
                   z = k*----- 
                           w

Now we're ready to substitute the numbers for all the letters except the
constant k from this: "z =8 when x =6, y =5 and w =10". Substituting:

                          6*5
                   8 = k*----- 
                           10


Solve for k:
                          30
                   8 = k*-----
                          10

                   8 = k*3

                  8
                 --- = k
                  3

Now go back to this equation:


                          xy
                   z = k*----- 
                           w

and substitute 3/8 for the constant k.


                        3   xy
                   z = ---*---- 
                        8    w

or

                        3xy
                   z = ----- 
                         8w

Now we substitute in x =3, y =4 and w = 5, to find z:


                        3(3)(4)
                   z = -------- 
                         8(5)

Then finish it up:

                        36
                   z = ---- 
                        40
          
Reduce the fraction:

                   
                         9
                   z = ---- 
                        10

The answer is 9/10.

[In many problems one of the types of variables "directly", "jointly",
or "inversely" variables are missing, in which case you put 1 for them.]

Edwin