Concept question - forces at different side of ladder

[homo-sapiens]

Homework Statement

The 87 kg painter in the figure below is using a large stepladder. The base of the ladder is 3 m wide, and the ladder is 7 m high. The painter is on a step that is 2.0 m above the floor. The horizontal bar of the ladder has a mass of 12 kg, and the entire ladder has a mass of 90 kg. Assume that the floor is frictionless.
http://puu.sh/cqbjn/de2f114817.png

Homework Equations

sum of torque
f=ma

The Attempt at a Solution

I would assume the forces at hinge b is different than the forces at hinge a since the man is on the side of hinge B and more importantly the bar has a mass so it's not massless thus the tension on both side shouldn't be the same... however on the answer key the reaction force on both hinges are the same.
http://puu.sh/cqbxK/5bfb197a8b.png
Can someone explain why the forces on both hinges the same??

 

[haruspex]

The forces (as vectors) are certainly not the same. Their magnitudes may happen to be the same. The question is, is there some clever argument that shows the magnitudes will be the same (without analysing the whole system)?
Consider just the horizontal bar. There are three forces on it, one known to be vertical and through the mid point. You can write down three statics equations: horizontal, vertical and rotational (torque). You can avoid involving the weight by just using the horizontal equation and moments about the centre. What do these two equations tell you?