How to solve?
x/10 = y/14 = z/35 = 1/(10x + 14y + 35z)
One method might be to solve x/10 = y/14 and x/10 = z/35 for y and z in terms of x. Then plug this into x/10 = 1/(10x + 14y + 35z), and solve for the value(s) of x.
Whatever method you use, it's likely gonna be messy, since this isn't linear.