Từ \(\begin{matrix}3x=y\Rightarrow\dfrac{x}{4}=\dfrac{y}{12}\\5y=4z\Rightarrow\dfrac{y}{12}=\dfrac{z}{15}\end{matrix}\Rightarrow\dfrac{x}{4}=\dfrac{y}{12}=\dfrac{z}{15}\)
Theo t/c dãy tỉ số bằng nhau ta có :
\(\dfrac{x}{4}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{6x}{24}=\dfrac{7y}{84}=\dfrac{8z}{120}=\dfrac{6x+7y+8z}{24+84+120}=\dfrac{456}{228}=2\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{4}=2\Rightarrow x=2.4=8\\\dfrac{y}{12}=2\Rightarrow y=2.12=24\\\dfrac{z}{15}=2\Rightarrow z=15.2=30\end{matrix}\right.\)
Vậy................
\(3x=y;5y=4z\Rightarrow\dfrac{x}{1}=\dfrac{y}{3};\dfrac{y}{4}=\dfrac{z}{5}\Rightarrow\dfrac{x}{4}=\dfrac{y}{12};\dfrac{y}{12}=\dfrac{z}{15}\Rightarrow\dfrac{x}{4}=\dfrac{y}{12}=\dfrac{z}{15}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{4}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{6x}{24}=\dfrac{7y}{84}=\dfrac{8z}{120}=\dfrac{6x+7y+8z}{24+84+120}=\dfrac{456}{228}=2\)
\(\dfrac{6x}{24}=2\Rightarrow6x=24.2=48\Rightarrow x=\dfrac{48}{6}=8\)
\(\dfrac{7y}{84}=2\Rightarrow7y=84.2=168\Rightarrow y=\dfrac{168}{7}=24\)
\(\dfrac{8z}{120}=2\Rightarrow8z=120.2=240\Rightarrow z=\dfrac{240}{8}=30\)
Vậy x=8 ; y=24 ; z=30
