# The Other AM-GM (Part 2)

Algebra Level 4

Let $$w, \space x, \space y,$$ and $$z$$ be positive real numbers, such that $$\dfrac{1}{w} + \dfrac{1}{x} + \dfrac{1}{z} = 5 - \dfrac{1}{y}$$. The minimum value of $$w^{4}x^{3}y^{2} z$$ is a form of $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. If $$\sqrt[3]{\dfrac{a}{b} } = \dfrac{c}{d}$$, where $$c$$ and $$d$$ are coprime positive integers, find $$b-a+d-c$$.

Note: Should you only use AM-GM?