Question

Tìm x,y,z biết:
a)\(\dfrac{2x}{3}=\dfrac{3y}{4}=\dfrac{4z}{5}\) và x + 2y+ 4z = 220

Answer 1

\(\dfrac{2x}{3}=\dfrac{3y}{4}=\dfrac{4z}{5}\)

\(\Leftrightarrow\dfrac{x}{\dfrac{3}{2}}=\dfrac{y}{\dfrac{4}{3}}=\dfrac{z}{\dfrac{5}{4}}\)

\(\Leftrightarrow\dfrac{x}{\dfrac{3}{2}}=\dfrac{2y}{\dfrac{8}{3}}=\dfrac{4z}{5}\)

Theo t,c dãy tỉ số bằng nhau ta có :

\(\dfrac{x}{\dfrac{3}{2}}=\dfrac{2y}{\dfrac{8}{3}}=\dfrac{4z}{5}=\dfrac{x+2y+4z}{\dfrac{3}{2}+\dfrac{8}{3}+5}=\dfrac{220}{\dfrac{55}{6}}=24\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{\dfrac{3}{2}}=24\\\dfrac{2y}{\dfrac{8}{3}}=24\\\dfrac{4z}{5}=24\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=36\\y=32\\z=30\end{matrix}\right.\)

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