c) Ta có:
\(\left\{{}\begin{matrix}3x=2y\Rightarrow\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{1}{5}.\frac{x}{2}=\frac{1}{5}.\frac{y}{3}\Rightarrow\frac{x}{10}=\frac{y}{15}\\7y=5z\Rightarrow\frac{y}{5}=\frac{z}{7}\Rightarrow\frac{1}{3}.\frac{y}{5}=\frac{1}{3}.\frac{z}{7}\Rightarrow\frac{y}{15}=\frac{z}{21}\end{matrix}\right.\)
\(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{21}=\frac{x-y+z}{10-15+21}=\frac{32}{16}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=20\\y=30\\z=42\end{matrix}\right.\)
d)Ta có:
\(\frac{2x}{3}=\frac{3y}{4}=\frac{4z}{5}\Rightarrow\frac{2x}{3}.60=\frac{3y}{4}.60=\frac{4z}{5}.60\)
\(\Rightarrow20.2x=15.3y=12.4z\)
\(\Rightarrow40x=45y=48z\Rightarrow\frac{x}{\frac{1}{40}}=\frac{y}{\frac{1}{45}}=\frac{z}{\frac{1}{48}}=\frac{x+y+z}{\frac{1}{40}+\frac{1}{45}+\frac{1}{48}}=\frac{49}{\frac{49}{720}}=720\)\(\Rightarrow\left\{{}\begin{matrix}x=18\\y=16\\z=15\end{matrix}\right.\)
e) Ta có:
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{2x-2+3y-6-\left(z-3\right)}{4+9-4}=\frac{2x-2+3y-6-z+3}{4+9-4}=\frac{2x+3y-z-5}{9}=\frac{50-5}{9}=\frac{45}{9}=5\)\(\Rightarrow\left\{{}\begin{matrix}x=11\\y=17\\z=23\end{matrix}\right.\)