What is the Equilibrium of a Uniform Rod with Unknown Weight?

[Yosty22]

Homework Statement

A uniform, 263-N rod that is 2.20m long carries a 225-N weight at its right end and an unknown weight W toward the left end (see attached figure). When W is placed 55.6-cm from the left end of the rod, the system just balances horizontally when the fulcrum is located 83.2-cm from the right end.

Homework Equations

Basic Torque equations + Newton's laws.

The Attempt at a Solution

I don't exactly know where to start. I know the sum of all torques has to be 0, but I'm not sure what numbers to use or where the mass of the rod comes into play. Can anybody help?

 

[rock.freak667]

If the length of the rod is 2.2 m, then its weight will act at the center of this rod. So it acts at what distance?

The sum of all moments (torques) about any point = 0 for equilibrium means that wherever you take moments, all should add up to zero. So consider taking moments about the fulcrum. What are the forces acting and their respective distances from the fulcrum?