Finding the Equilibrium of Roller Forces: How Do We Solve This?

[SteelDirigibl]

Homework Statement

Homework Equations

The Attempt at a Solution

I'm a little lost how to begin. I know these forces at B and C add up to 31lbs, but I don't know where else to go. I understand the simpler ones like center of gravity on a car and forces on the wheels but this one loses me

 

[tiny-tim]

Hi SteelDirigibl!

Hint: moments ​

 

[SteelDirigibl]

I think I just needed to get some sleep and work on it!

So I did moment about C first, where 31*sin(45)5.5=5.2*x

where x is the force at b.

Then we do the same thing but for the moment about b, so 31*(sin(45)5.5+5.2)=5.2x
where x is the force at C.

annnd I got it right