# Give me a four, give me a two

Algebra Level 5

Let $$x,y,z$$ be positive real numbers such that: \begin{align} xyz&=945 \\ x(y+1)+y(z+1)+z(x+1)&=385. \end{align} If the minimum possible value of $$z+\frac{y}{2}+\frac{x}{4}$$ can be written as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a+b$$?

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