\(\dfrac{2x}{3}=\dfrac{3y}{4}=\dfrac{4z}{5}\Rightarrow\dfrac{x}{\dfrac{3}{2}}=\dfrac{y}{\dfrac{4}{3}}=\dfrac{z}{\dfrac{5}{4}}\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{\dfrac{3}{2}}=\dfrac{y}{\dfrac{4}{3}}=\dfrac{z}{\dfrac{5}{4}}=\dfrac{x+y+z}{\dfrac{3}{2}+\dfrac{4}{3}+\dfrac{5}{4}}=\dfrac{98}{\dfrac{49}{12}}=24\\ \Rightarrow\left\{{}\begin{matrix}x=24\cdot\dfrac{3}{2}=36\\y=24\cdot\dfrac{4}{3}=32\\z=24\cdot\dfrac{5}{4}=30\end{matrix}\right.\)
\(\dfrac{2x}{3}=\dfrac{3y}{4}=\dfrac{4z}{5}\Rightarrow\dfrac{x}{18}=\dfrac{y}{16}=\dfrac{z}{15}\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{18}=\dfrac{y}{16}=\dfrac{z}{15}=\dfrac{x+y+z}{18+16+15}=\dfrac{98}{49}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=2.18=36\\y=2.16=32\\z=2.15=30\end{matrix}\right.\)
