Ta có: \(\frac{2x}{3}=\frac{2y}{4}=\frac{4z}{5}.\)
\(\Rightarrow\frac{x}{\frac{3}{2}}=\frac{y}{\frac{4}{2}}=\frac{z}{\frac{5}{4}}.\)
\(\Rightarrow\frac{x}{\frac{3}{2}}=\frac{y}{2}=\frac{z}{\frac{5}{4}}\) và \(x+y+z=49.\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\frac{x}{\frac{3}{2}}=\frac{y}{2}=\frac{z}{\frac{5}{4}}=\frac{x+y+z}{\frac{3}{2}+2+\frac{5}{4}}=\frac{49}{\frac{19}{4}}=\frac{196}{19}.\)
\(\Rightarrow\left\{{}\begin{matrix}\frac{x}{\frac{3}{2}}=\frac{196}{19}\Rightarrow x=\frac{196}{19}.\frac{3}{2}=\frac{294}{19}\\\frac{y}{2}=\frac{196}{19}\Rightarrow y=\frac{196}{19}.2=\frac{392}{19}\\\frac{z}{\frac{5}{4}}=\frac{196}{19}\Rightarrow z=\frac{196}{19}.\frac{5}{4}=\frac{245}{19}\end{matrix}\right.\)
Vậy \(\left(x;y;z\right)=\left(\frac{294}{19};\frac{392}{19};\frac{245}{19}\right).\)
Chúc bạn học tốt!