Question

Tìm x,y,x biết:

\(\frac{x}{2}=\frac{y}{3};\frac{y}{7}=\frac{z}{4}\)và x+y-z=69

Ai nhanh mik tick ba cái nè

Answer 1

\(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{14}=\frac{y}{21}\)

\(\frac{y}{7}=\frac{z}{4}\Rightarrow\frac{y}{21}=\frac{z}{12}\)

\(\Leftrightarrow\frac{x}{14}=\frac{y}{21}=\frac{z}{12}=\frac{x+y-z}{14+21-12}=\frac{69}{23}=3\)

\(\Rightarrow x=52;y=63;z=36\)

Answer 2

\(\hept{\begin{cases}\frac{x}{2}=\frac{y}{3}\\\frac{y}{7}=\frac{z}{4}\end{cases}\Rightarrow\hept{\begin{cases}\frac{x}{14}=\frac{y}{21}\\\frac{y}{21}=\frac{z}{12}\end{cases}\Rightarrow}\frac{x}{14}=\frac{y}{21}=\frac{z}{12}}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\frac{x}{14}=\frac{y}{21}=\frac{z}{12}=\frac{x+y-z}{14+21-12}=\frac{69}{23}=3\)

\(\Rightarrow\hept{\begin{cases}x=3.14=42\\y=3.21=63\\z=3.12=36\end{cases}}\)

Answer 3

Ta có:

\(\frac{x}{2}=\frac{y}{3};\frac{y}{7}=\frac{z}{4}\)

=> \(\frac{x}{14}=\frac{y}{21};\frac{y}{21}=\frac{z}{12}\)

=> \(\frac{x}{14}=\frac{y}{21}=\frac{z}{12}=\frac{x+y-z}{14+21-12}=\frac{69}{23}=3\)

Từ trên ta có:

\(\frac{x}{14}=3=>x=3.14=42\)

\(\frac{y}{21}=3=>y=3.21=63\)

\(\frac{z}{12}=3=>z=3.12=36\)

Vậy x = 42

       y = 63

       z = 36

ỦNG HỘ NHA

Answer 4

Ta có : \(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{14}=\frac{y}{21}\left(1\right)\)

\(\frac{y}{7}=\frac{z}{4}\Rightarrow\frac{y}{21}=\frac{z}{12}\left(2\right)\)

Từ ( 1 ) và ( 2 ) => \(\frac{x}{14}=\frac{y}{21}=\frac{z}{12}\)

Theo tính chất dãy tỉ số bằng nhau ta có :

\(\frac{x}{14}=\frac{y}{21}=\frac{z}{12}=\frac{x+y-z}{14+21-12}=\frac{69}{23}=3\)

\(\frac{x}{14}=3\Rightarrow x=3\times14=42\)

\(\frac{y}{21}=3\Rightarrow y=3\times21=63\)

\(\frac{z}{12}=3\Rightarrow z=3\times12=36\)

Vậy x = 42 ; y = 63 ; z = 36