Theo đề ta có: \(\dfrac{x}{1}=\dfrac{y}{\dfrac{1}{4}}=\dfrac{y+z}{\dfrac{5}{2}}\)

và x + y + z = 280

Áp dụng t/c của dãy tỉ số bằng nhau có:

\(\dfrac{x}{1}=\dfrac{y}{\dfrac{1}{4}}=\dfrac{y+z}{\dfrac{5}{2}}=\dfrac{x+y+y+z}{1+\dfrac{1}{4}+\dfrac{5}{2}}=\dfrac{280+y}{3,75}\)

\(\Rightarrow\dfrac{y}{\dfrac{1}{4}}=\dfrac{280+y}{3,75}\Rightarrow3,75y=\dfrac{1}{4}\left(280+y\right)\)

\(\Rightarrow3,75y=70+\dfrac{1}{4}y\Rightarrow3,75y-\dfrac{1}{4}y=70\)

\(\Rightarrow3,5y=70\Rightarrow y=\dfrac{70}{3,5}=20\)

Có: \(\dfrac{x}{1}=\dfrac{y}{\dfrac{1}{4}}\Rightarrow\dfrac{x}{1}=\dfrac{20}{\dfrac{1}{4}}\Rightarrow\dfrac{1}{4}x=20\Rightarrow x=20:\dfrac{1}{4}=80\)

\(\Rightarrow z=280-\left(x+y\right)=280-100=180\)

Vậy x = 80; y = 20; z = 180