\(\dfrac{1}{2}a=\dfrac{2}{3}b=\dfrac{3}{4}c\Leftrightarrow\dfrac{a}{2}=\dfrac{b}{\dfrac{3}{2}}=\dfrac{c}{\dfrac{4}{3}}\)
Áp dụng tc dtsbn:
\(\dfrac{a}{2}=\dfrac{b}{\dfrac{3}{2}}=\dfrac{c}{\dfrac{4}{3}}=\dfrac{a-b}{2-\dfrac{3}{2}}=\dfrac{15}{\dfrac{1}{2}}=30\\ \Leftrightarrow\left\{{}\begin{matrix}a=60\\b=30\cdot\dfrac{3}{2}=45\\c=30\cdot\dfrac{4}{3}=40\end{matrix}\right.\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{a}{2}=\dfrac{b}{\dfrac{3}{2}}=\dfrac{c}{\dfrac{4}{3}}=\dfrac{a-b}{2-\dfrac{3}{2}}=\dfrac{15}{\dfrac{1}{2}}=30\)
Do đó: a=60; b=45; c=40