Question

TIm x y z
2x/3 = 3y/4 = 4z/5 va x + y + z = 49

Answer 1

Từ \(\frac{2x}{3}=\frac{3y}{4}=\frac{4z}{5}\Rightarrow\frac{x}{\frac{3}{2}}=\frac{y}{\frac{4}{3}}=\frac{z}{\frac{5}{4}}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{x}{\frac{3}{2}}=\frac{y}{\frac{4}{3}}=\frac{z}{\frac{5}{4}}=\frac{x+y+z}{\frac{3}{2}+\frac{4}{3}+\frac{5}{4}}=\frac{49}{\frac{49}{12}}=12\)

\(\Rightarrow\left\{\begin{matrix}\frac{x}{\frac{3}{2}}=12\Rightarrow x=12\cdot\frac{3}{2}=18\\\frac{y}{\frac{4}{3}}=12\Rightarrow y=12\cdot\frac{4}{3}=16\\\frac{z}{\frac{5}{4}}=12\Rightarrow z=12\cdot\frac{5}{4}=15\end{matrix}\right.\)