$\dfrac{x}{2}=\dfrac{y}{3}\Leftrightarrow\dfrac{x}{8}=\dfrac{y}{12}$
$\dfrac{y}{4}=\dfrac{z}{5}\Leftrightarrow\dfrac{y}{12}=\dfrac{z}{15}$
$\Leftrightarrow\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}$
$\Leftrightarrow\dfrac{2x}{16}=\dfrac{3y}{36}=\dfrac{4z}{60}$
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
$\dfrac{2x}{16}=\dfrac{3y}{36}=\dfrac{4z}{60}=\dfrac{2x-3y+4z}{16-36+60}=\dfrac{330}{40}=\dfrac{33}{4}$
$\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{8}=\dfrac{33}{4}\Leftrightarrow x=66\\\dfrac{y}{12}=\dfrac{33}{4}\Leftrightarrow y=99\\\dfrac{z}{15}=\dfrac{33}{4}\Leftrightarrow z=123,75\end{matrix}\right.$
