I'm guessing that you were off by a factor of 2. In the Hooke's Law equation (F = -kx) where force is generated by gravity, F represents the AVERAGE force, not the peak force. Force is not constant as the the spring is compressed from its relaxed length to its new equilibrium point with the...
The reason why the two answers are different is that in the Hooke's Law equation, F represents the AVERAGE force, not the peak force. Force is not constant as the the spring extends from its relaxed length to its new equilibrium point with the weight hanging on it.
The problem assumes that...