# Simple Inequality 3

Algebra Level 3

$$a,b$$ and $$c$$ are three positive real numbers such that $$a+b+c=n$$.

What is the smallest possible value of $$n$$ such that

$(ab+bc+ca)\left(\dfrac{a}{2b+3c}+\dfrac{b}{2c+3a}+\dfrac{c}{2a+3b}\right)\ge 20$

for all possible ordered triplets $$(a,b,c)?$$

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