Ta có: \(3x=5y=7z\) \(\Leftrightarrow\) \(\dfrac{x}{\dfrac{1}{3}}=\dfrac{y}{\dfrac{1}{5}}=\dfrac{z}{\dfrac{1}{7}}\) và \(x+y-z=41\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{\dfrac{1}{3}}=\dfrac{y}{\dfrac{1}{5}}=\dfrac{z}{\dfrac{1}{7}}=\dfrac{x+y-z}{\dfrac{1}{3}+\dfrac{1}{5}-\dfrac{1}{7}}=\dfrac{41}{\dfrac{41}{105}}=105\)
\(\dfrac{x}{\dfrac{1}{3}}=105\Rightarrow x=105.\dfrac{1}{3}=35\)
\(\dfrac{y}{\dfrac{1}{5}}=105\Rightarrow y=105.\dfrac{1}{5}=21\)
\(\dfrac{z}{\dfrac{1}{7}}=105\Rightarrow z=105.\dfrac{1}{7}=15\)
Vậy \(x=35\); \(y=21\); \(z=15\)
\(\Rightarrow\dfrac{x}{5}=\dfrac{y}{3}\) , \(\dfrac{y}{7}=\dfrac{z}{5}\) \(\Rightarrow\dfrac{x}{35}=\dfrac{y}{21},\dfrac{y}{21}=\dfrac{z}{15}\) \(\Rightarrow\dfrac{x}{35}=\dfrac{y}{21}=\dfrac{z}{15}\) \(=\) \(\dfrac{x+y-z}{35+21-15}\) = \(\dfrac{41}{11}\) ta có \(\dfrac{x}{35}=\dfrac{41}{11}\Rightarrow x=41\times35\div11=130,\left(45\right)\) \(y=130,\left(45\right)\times3\div5\) \(=78,\left(27\right)\) \(z=78.\left(27\right)\times5\div7=55.\left(90\right)\)