\(8x = 9y = 12z \Rightarrow \dfrac{8x}{144} = \dfrac{9y}{144} = \dfrac{12z}{144} \\\Leftrightarrow \dfrac{x}{18} = \dfrac{y}{16} = \dfrac{z}{12} = \dfrac{x + y + z}{18 + 16+12} = \dfrac{69}{46}\)
\(\Leftrightarrow x = \dfrac{18.69}{46} = 27\\
\Leftrightarrow y = \dfrac{16.69}{46} = 24\\
\Leftrightarrow z = \dfrac{12.69}{46} = 18\)