Đáp án:
\[x = 20;\,\,\,y = 30;\,\,\,z = 42\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\dfrac{x}{2} = \dfrac{y}{3} \Leftrightarrow \dfrac{1}{5}.\dfrac{x}{2} = \dfrac{1}{5}.\dfrac{y}{3} \Leftrightarrow \dfrac{x}{{10}} = \dfrac{y}{{15}}\\
\dfrac{y}{5} = \dfrac{z}{7} \Leftrightarrow \dfrac{1}{3}.\dfrac{y}{5} = \dfrac{1}{3}.\dfrac{z}{7} \Leftrightarrow \dfrac{y}{{15}} = \dfrac{z}{{21}}\\
\Rightarrow \dfrac{x}{{10}} = \dfrac{y}{{15}} = \dfrac{z}{{21}}
\end{array}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\begin{array}{l}
\dfrac{x}{{10}} = \dfrac{y}{{15}} = \dfrac{z}{{21}} = \dfrac{{x + y + z}}{{10 + 15 + 21}} = \dfrac{{92}}{{46}} = 2\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{x}{{10}} = 2\\
\dfrac{y}{{15}} = 2\\
\dfrac{z}{{21}} = 2
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 20\\
y = 30\\
z = 42
\end{array} \right.
\end{array}\)
Vậy \(x = 20;\,\,\,y = 30;\,\,\,z = 42\)
