Theo đề bài, ta có: \(\dfrac{2}{3}x=\dfrac{3}{5}y\)
\(\Rightarrow\dfrac{2x}{3}=\dfrac{3y}{5}\)
\(\Rightarrow\dfrac{2x}{18}=\dfrac{3y}{30}\)
\(\Rightarrow\dfrac{x}{9}=\dfrac{y}{10}\)
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
\(\dfrac{x}{9}=\dfrac{y}{10}=\dfrac{x+y}{9+10}=\dfrac{38}{19}=2\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{x}{9}=2\Rightarrow x=18\\\dfrac{y}{10}=2\Rightarrow y=20\end{matrix}\right.\)
\(\dfrac{2}{3}x=\dfrac{3}{5}y\Leftrightarrow\dfrac{x}{\dfrac{3}{2}}=\dfrac{y}{\dfrac{5}{3}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{\dfrac{3}{2}}=\dfrac{y}{\dfrac{5}{3}}=\dfrac{x+y}{\dfrac{3}{2}+\dfrac{5}{3}}=\dfrac{38}{\dfrac{19}{6}}=12\)
\(\Rightarrow\left\{{}\begin{matrix}x=12.\dfrac{3}{2}=18\\y=12.\dfrac{5}{3}=20\end{matrix}\right.\)
