\(a,\Rightarrow7\left(37-x\right)=3\left(x+13\right)\\ \Rightarrow259-7x=3x+39\\ \Rightarrow10x=220\Rightarrow x=22\\ b,2x=3y\Rightarrow\dfrac{x}{3}=\dfrac{y}{2}\Rightarrow\dfrac{x}{21}=\dfrac{y}{14}\\ 5y=7z\Rightarrow\dfrac{y}{7}=\dfrac{z}{5}\Rightarrow\dfrac{y}{14}=\dfrac{z}{10}\\ \Rightarrow\dfrac{x}{21}=\dfrac{y}{14}=\dfrac{z}{10}\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{21}=\dfrac{y}{14}=\dfrac{z}{10}=\dfrac{3x}{63}=\dfrac{5y}{70}=\dfrac{7z}{70}=\dfrac{3x+5y-7z}{63+70-70}=\dfrac{30}{63}=\dfrac{10}{21}\\ \Rightarrow\left\{{}\begin{matrix}x=10\\y=\dfrac{20}{3}\\z=\dfrac{100}{21}\end{matrix}\right.\)
\(c,\Rightarrow\dfrac{x}{2}=\dfrac{2y}{3}=\dfrac{3z}{4}\Rightarrow\dfrac{x}{2}=\dfrac{y}{\dfrac{3}{2}}=\dfrac{z}{\dfrac{4}{3}}\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{2}=\dfrac{y}{\dfrac{3}{2}}=\dfrac{z}{\dfrac{4}{3}}=\dfrac{x-y}{2-\dfrac{3}{2}}=\dfrac{15}{\dfrac{1}{2}}=30\\ \Rightarrow\left\{{}\begin{matrix}x=60\\y=45\\z=40\end{matrix}\right.\)
\(d,\Rightarrow\dfrac{x}{\dfrac{1}{5}}=\dfrac{y}{\dfrac{1}{8}}=\dfrac{z}{\dfrac{1}{20}}\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{\dfrac{1}{5}}=\dfrac{y}{\dfrac{1}{8}}=\dfrac{z}{\dfrac{1}{20}}=\dfrac{x-y-z}{\dfrac{1}{5}-\dfrac{1}{8}-\dfrac{1}{20}}=\dfrac{3}{\dfrac{1}{40}}=120\\ \Rightarrow\left\{{}\begin{matrix}x=24\\y=15\\z=6\end{matrix}\right.\)
\(e,\Rightarrow\dfrac{x-4}{4}=\dfrac{y-3}{3}\)
Áp dụng t/c dtsbn:
\(\dfrac{x-4}{4}=\dfrac{y-3}{3}=\dfrac{x-4-y+3}{4-3}=\dfrac{5-1}{1}=4\\ \Rightarrow\left\{{}\begin{matrix}x-4=16\\y-3=12\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=20\\y=15\end{matrix}\right.\)
