Question

x/3=y/4 ; y/5=z/6 ; x-2y+3z=141

Answer 1

\(\dfrac{x}{3}=\dfrac{y}{4}\Rightarrow\dfrac{x}{15}=\dfrac{y}{20}\\ \dfrac{y}{5}=\dfrac{z}{6}\Rightarrow\dfrac{y}{20}=\dfrac{z}{24}\\ \Rightarrow\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{24}\)

Áp dụng t/c dtsbn ta có:

\(\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{24}=\dfrac{x-2y+3z}{15-2.20+3.24}=\dfrac{141}{47}=3\)

\(\dfrac{x}{15}=3\Rightarrow x=45\\ \dfrac{y}{20}=3\Rightarrow y=60\\ \dfrac{z}{24}=3\Rightarrow z=72\)