Where I always start is by drawing a picture of what's going on. Then I start drawing a free body diagram. The reason I tilted the axis is because you always want your x-axis or y-axis parallel to the motion.
For instance the box was going up the ramp so I decided to let the x-axis be...
Yep it looks like you did it right. Think about it. 100 kg isn't light. Not just that but you're pushing against the ramp you're not pushing at an angle so that makes the force that the ramp feels go up.
***100kg is 220 lbs!***
Oh yeah sorry haha. Well n is the normal force because it's always perpendicular to the surface. Fa is force applied and Fg is the force of gravity.
Looking at the summation of Fx you can easily solve for Fa by adding both sides by Fgsintheta and dividing costheta.
Fa = Fgsinθ/cosθ
The...