Ta có:
\(4x=5y\)
\(\Rightarrow\dfrac{x}{5}=\dfrac{y}{4}\)
\(\Rightarrow\dfrac{x}{20}=\dfrac{y}{16}\left(1\right)\)
Ta lại có:
\(7x=4z\)
\(\Rightarrow\dfrac{x}{4}=\dfrac{z}{7}\)
\(\Rightarrow\dfrac{x}{20}=\dfrac{z}{35}\left(2\right)\)
Từ (1) và (2) suy ra:
\(\dfrac{x}{20}=\dfrac{y}{16}=\dfrac{z}{35}\)
\(=\dfrac{x}{20}=\dfrac{2y}{32}=\dfrac{z}{35}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\dfrac{x}{20}=\dfrac{2y}{32}=\dfrac{z}{35}\)
\(=\dfrac{x+2y+z}{20+32+35}=\dfrac{80}{87}\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{20}=\dfrac{80}{87}\\\dfrac{y}{16}=\dfrac{80}{87}\\\dfrac{z}{35}=\dfrac{80}{87}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{80}{87}.20\\y=\dfrac{80}{87}.16\\z=\dfrac{80}{87}.35\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{1600}{87}\\y=\dfrac{1280}{87}\\z=\dfrac{2800}{87}\end{matrix}\right.\)