Question

Cho \(\dfrac{1}{2}X\)=\(\dfrac{2}{3}y\)=\(\dfrac{3}{4}z\) và x-y=15

Tính x;y;z

Answer 1

\(\dfrac{1}{2}x=\dfrac{2}{3}y=\dfrac{3}{4}z\)

\(\Leftrightarrow\dfrac{x}{2}=\dfrac{y}{\dfrac{3}{2}}=\dfrac{z}{\dfrac{4}{3}}\)

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

\(\dfrac{x}{2}=\dfrac{y}{\dfrac{3}{2}}=\dfrac{z}{\dfrac{4}{3}}=\dfrac{x-y}{2-\dfrac{3}{2}}=\dfrac{15}{\dfrac{1}{2}}=30\)

\(\Rightarrow\left\{{}\begin{matrix}x=30.2=60\\y=30.\dfrac{3}{2}=45\\z=30.\dfrac{4}{3}=40\end{matrix}\right.\)