# Irreducible Ratio

Geometry Level pending

Let $$ABC$$ be a triangle and let $$a$$, $$b$$ and $$c$$ be the lengths of the sides opposite to the vertices $$A$$, $$B$$ and $$C$$, respectively. If $a - 4b + c = 0, 2a + b - 2c = 0 ,$ then $$\sin A : \sin B : \sin C$$ can be expressed as an irreducible ratio $$p:q:r$$, where $$p$$, $$q$$ and $$r$$ are positive integers. What is $$p+q+r?$$

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