Row Reduction & Rank · Medium problem

When propane burns completely, $a\,C_3H_8 + b\,O_2 \to c\,CO_2 + d\,H_2O$. Balancing the carbon, hydrogen, and oxygen atoms gives a homogeneous linear system in $a, b, c, d$ (one equation per element). Using the smallest positive integers satisfying it, with $a = 1$, find $a+b+c+d$.