SOLUTION: If y varies directly as x and inversely as z, what is the effect on y of doubling x and z?

For all proportion problems, start with this:

Varying           "directly" or product of "jointlys" or 1 if none 
quantity  = k · ----------------------------------------------------------
                inversely variable or product of "inverselys" or 1 if none

In this problem the varying quantity is y.
the "directly" is x.  We have one inversely, z.  So we have 
on top and p on the bottom:

        y = k·

Suppose at first substitute x=a and z=b

(1)     y = k·

Now let's double a as 2a and double b as 2b and substitute 
x = 2a and z=2b

        y = k·

We can cancel the 2's

        y = k·

(2)     y = k·

Now we compare (2) with (1) and we see they are identical.

Answer: There is no effect.

Edwin