Each variable, a to f, is a distinct prime number. Four variables (b to e) may be deduced with a combination of mathematical and cryptic reasoning and should then be arranged to create a sequence. Two variables which extend the sequence at either end (a and f) are not clued and must be extrapolated. Solve for the sum of the variables a+b+c+d+e+f.
(Solutions are always the lowest possible positive integer values).
3x = 4y = 5z
b = 2c + e - z
c = x - y
d = Number of partners embracing woman (5)
e = Number Ten and their spin! (8)
[I had fun writing this, I just hope it works!]