# Is It Really Balancing The Coefficients?

Algebra Level 5

Let $$a$$, $$b$$ and $$c$$ be positive real numbers satisfying $(a+b+c)\left(\frac {1}{a} + \frac {1}{b} +\frac {1}{c}\right) =16$ If the smallest and largest possible values of $\frac {a}{b} + \frac {b}{c} +\frac {c}{a}$ are $$m$$ and $$M$$ respectively, then find the value of $$\lfloor 100 (m+2M )\rfloor$$.

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