Static Equilibrium and Torque Homework Question

[VincentweZu]

Homework Statement

A hiker, who weighs 985 N is strolling through the woods and crosses a small horizontal bridge. the bridge is uniform, weighs 3610 N, and rests on two concrete supports, one at each end. he stops one - fifth of the way along the bridge. What is the magnitude of the force that a concrete support exerts on the bridge:

a) at the near end and
b) at the far end

Answer to a) 2590, b) 2010

Homework Equations

Static Equilibrium: ƩT = 0
T = Frsinθ

The Attempt at a Solution

Took opposite support as pivot point such that Fn x r is the CCW torque where r is the length of bridge
Expressed distance from the pivot point of each force in terms of r
Wrote net torque equation, crossed out r from both sides
Solved for Fn

a) Fn = 985 x 4/5 + 3610 x 1/2
Fn = 2593 N
b) Fn = 985 x 1/5 + 3610 x 1/2
Fn = 2002 N

I am not sure whether or not my approach to this problem is correct.

 

[Delphi51]

Yes, looks good.
You can also sum the vertical forces - total must be zero - as a check.
2593 rounds to 2590, but I don't see how to get 2010 from 2002.