Varies jointly means there exists a constant k such that:

z = kxy

We're given z = 3 when x = 3 and y = 15, so we have:

3 = 15 * 3 * k

3 = 45k

Using our equation solver, we see that:

k = 1/15

So our joint variation equation is:

z = xy/15

Then we're asked to find z when x = 6 and y = 9

z = 6 * 9 / 15

z = 54/15

z =

**18/5**