# Combustion Secret Formula

Chemistry Level pending

The compound $$C_aH_bO_c$$ reacts completely with oxygen gas to produce carbon dioxide and water. For every mole of $$C_aH_bO_c$$ reacted, $$xa+yb-zc$$ moles of oxygen are also combusted.

If $$x+y+z$$ can be written in the form $$\frac{M}{N},$$ where $$M$$ and $$N$$ are positive coprime integers, find $$M+N.$$

You may assume that the compound $$C_aH_bO_c$$ exists, and that $$a$$ and $$b$$ are positive integers while $$c$$ is a non-negative integer.

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