\(\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{x}{15}=\frac{y}{20}_{\left(1\right)}\)

\(\frac{y}{5}=\frac{z}{6}\Rightarrow\frac{y}{20}=\frac{z}{24}_{\left(2\right)}\)

\(T\text{ừ}_{\left(1\right)};_{\left(2\right)}\Rightarrow\frac{x}{15}=\frac{y}{20}=\frac{z}{24}\)

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

\(\frac{x}{15}=\frac{y}{20}=\frac{z}{24}=\frac{x+y-z}{15+20-24}=\frac{11}{11}=1\)

\(\Rightarrow\hept{\begin{cases}\frac{x}{15}=1\Rightarrow x=15\\\frac{y}{20}=1\Rightarrow y=20\\\frac{z}{24}=1\Rightarrow z=24\end{cases}}\)

TL

x = 15,

y = 20,

z = 24;

HT

\(\frac{x}{5}=\frac{4,2}{8,4}\)

\(\frac{x}{5}=\frac{1}{2}\)

\(\Leftrightarrow\)\(2x=5\)

\(\Leftrightarrow\)\(x=\frac{5}{2}\)

x= 25,5

hok tốt

ư ư ư ư ư ư ư ư thôi bỏ

Từ \(2x=3y\)\(\Rightarrow\)\(\frac{x}{3}=\frac{y}{2}=\frac{x}{3}.\frac{1}{7}=\frac{y}{2}.\frac{1}{7}\)\(\Rightarrow\)\(\frac{x}{21}=\frac{y}{14}\)( 1 )

Từ \(5y=7z\)\(\Rightarrow\)\(\frac{y}{7}=\frac{z}{5}=\frac{y}{7}.\frac{1}{2}=\frac{z}{5}.\frac{1}{2}\)\(\Rightarrow\)\(\frac{y}{12}=\frac{z}{10}\)( 2 )

Từ ( 1 ) và ( 2 ) suy ra : \(\frac{x}{21}=\frac{y}{14}=\frac{z}{10}\)

Đặt \(\frac{x}{21}=\frac{y}{14}=\frac{z}{10}=k\)\(\Rightarrow\hept{\begin{cases}x=21k\\y=14k\\z=10k\end{cases}}\)

Thay vào ta được :

\(2.21k-3.14k+4.10k=350\)

\(42k-42k+40k=350\)

\(40k=350\)

\(k=\frac{35}{4}\)

\(\Rightarrow\hept{\begin{cases}x=21.\frac{35}{4}\\y=14.\frac{35}{4}\\z=10.\frac{35}{4}\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=\frac{735}{4}\\y=\frac{245}{2}\\z=\frac{175}{2}\end{cases}}\)