How to Prove the Weighted Centroid Formula for Parallel Forces?

[BigCheese234]

Given the formula for the weighted centroid, C of a system of parallel forces
Fi acting at points Pi, show that two weights W and 3W, acting respectively
at points P1, P2, are together equivalent to a single weight 4W acting at P,
where P lies on the line segment joining P1 to P2 and P1 P : P P2 = 3 : 1.OC = (Ʃi opi.Fi)/ (ƩFi)Any one know how to prove it ? revising and this came up in a test last year its not in my notes?

 

[haruspex]

Is that the formula as you're given it? The forces are vectors, so it would more logically be written
OC. (ƩFi) = (Ʃi opi.Fi)
You have the choice of where to place the origin. Where will you place it? Having done that, can you fill in the RHS of the formula using the W & 3W set-up?