Mechanics on static particles - where did i go wrong?

[wduk]

So i got this wrong but not sure where my error is.

I have a static particle with three forces acting upon it:

H => Magnitude 70N directed vertically upwards.
F => Directed left and down 120 deg to the vertical. Unknown magnitude.
G => Directed right and down 150 deg to the vertical. Unknown magnitude.

I'm told to the find the magnitudes of F and G in Newtons (N).

So G and F directions are:

|G| cos(300 deg) i + |G| sin(300 deg) j
using |G| = G
= 1/2 G i + -(sqrt(3)/2) G j

|F| cos(210 deg) i + |F| sin(210 deg) j
using |F| = F
= -(sqrt(3)/2)F i + (-1/2)F j

Now i use simultaneous equations to solve them since the particle is static:

Equation 1) 1/2 G - (sqrt(3)/2) F = 0

Equation 2) -(sqrt(3)/2) G - 1/2 F + 70 = 0

I multiplied equation 2 by sqrt(3) to get equation 3.

Equation 3) -3/2 G - (sqrt(3)/2) F + 70sqrt(3) = 0

Now i subtract Equation 1 by Equation 3 to cancel F and thus solve G:
-(3/2)G - (1/2)G - 70sqrt(3) = 0
-2G = 70sqrt(3)

Equation 4) G = -35sqrt(3) N (this is correct according to my answers)


Now i plug equation 4 to equation 2 to solve for F:

-(sqrt(3)/2) * -35sqrt(3) + 70 - (1/2) F = 0
245/2 - (1/2) F = 0
-(1/2) F = -242/2
F = (-242/2) / (-1/2)
F = 245 N

But my answer sheet says F is 35 N.

So i clearly went wrong calculating F but am not sure what part i did wrong?