in the answer why to they add the portion that is necessary to counter the gravitational force, instead of subtracting it

take it step by step

break down the weight vector into vx and vy components

the vx component is the one we care about mgsin(ø) -> 10*10*sin(30) = 50

that is the force that is parallel to the plane

there is acceleration .:. there is a net force

therefore ma = force applied - weight vector (they are subtracted b/c the force applied is to the right whereas the weight vector is to the left .:. they are acting in opposite directions)

ma = 10*2

20 = x - 50

.:. the force applied is 70 N