Assume that a varies directly with z. if a = 30 when z = 5, find a when z = 9.

We can this two ways:

1) If A = 30 when Z = 5, then A = 6Z or A = 6*z

So if Z = 9, 9 * 6 = 54. A = 54. 

2) You can set up a proportion:
where x = the unknown A-value.

Crossmultiply:
5x = 30*9
5x = 270

Divide by 5 on both sides to isolate the variable
x = 54

54 is your A value when Z = 9.

Either way you solve it, your answer is 54.