To be directly proportional, the relationship must follow

` ` to be inversely proportional the relationship must follow

` ` combining these relationships we get

` `

We can use the initial conditions to determine the value for k:

`k = (PIT)/(WS) = (100*200*500)/(2000*50) = 100` this gives us the general equation:

`P = 100(WS)/(IT)` This can now be used to answer the question:

`P = 100(500*30)/(100*3) = 5000`

Alternate solution:

Label given quantities with subscript 2 and new quantities with subscript 1.

`k = (P_1I_1T_1)/(W_1S_1)` and `k = (P_2I_2T_2)/(W_2S_2)` by the transitive property of equality

`(P_1I_1T_1)/(W_1S_1) = (P_2I_2T_2)/(W_2S_2)` solving for `P_1` gives

`P_1 = (P_2I_2T_2W_1S_1)/(W_2S_2I_1T_1) = (100*200*500*500*30)/(2000*50*100*3) = 5000`

` `