Confused about answer key's solution to a work/energy problem

[physics801]

I'm studying for my college's physics placement and I'm frustrated because I don't get the solution to problem 1d.

Homework Statement

The problem is here: http://ocw.edu.ht/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/exams/exam_2.pdf

Solution manual is here: http://ocw.edu.ht/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/exams/quiz2_sol.pdf

The Attempt at a Solution

I drew a mspaint diagram of what I have: http://cl.ly/image/3b1o082l1k3a (x_{max} is defined in 1a, which is in the soln manual)

Basically since gravity is opposing the direction of travel (up the ramp), I think the solution to 1d(i) should be work=-mg(h-h_{max})=-mgsin\theta(x-x_{max}). However the solution manual has the same thing except x_{max}-x in the parentheses. Why is this? Shouldn't it be final - initial, which means x-x_{max} in the parentheses?

edit: I also have the same question for 1d(ii) and (iii) but hopefully it will be answered by explaining (i)

 

[haruspex]

You have to decide which way is positive and stick to it.
If the force due to gravity is being taken as negative along the slope then the positive direction is up the slope. But x is measured down the slope, so it's (-x) - (-x_max)
It is always a good idea to sanity-check the sign of a result. It is clear that the work done by gravity here is negative.

 

[/AH]

Look at the direction of x, what does x mean in terms of the spring?

 

[physics801]

You have to decide which way is positive and stick to it.
If the force due to gravity is being taken as negative along the slope then the positive direction is up the slope. But x is measured down the slope, so it's (-x) - (-x_max)
It is always a good idea to sanity-check the sign of a result. It is clear that the work done by gravity here is negative.

Oh whoops, I completely missed that. Thanks for the help!