Ta có: x+y+z =180
<=>5x+y=180
Ta lại có \(\dfrac{x}{3}=\dfrac{5x}{15}=\dfrac{y}{25}\)
Áp dụng dãy tỉ số bằng nhau:
k=\(\dfrac{x}{3}=\dfrac{5x}{15}=\dfrac{y}{25}\)=\(\dfrac{5x+y}{15+25}=\dfrac{180}{40}=\dfrac{9}{2}\)
=>k=\(\dfrac{9}{2}\)
Do đó: \(\dfrac{x}{3}=\dfrac{9}{2}=>x=\dfrac{27}{2}\)
\(\dfrac{y}{25}=\dfrac{9}{2}=>y=\dfrac{225}{2}\)
z=4x=4*\(\dfrac{27}{2}=54\)
\(z=4x\)
\(\Rightarrow x+y+z=x+4x+y=180\)
\(\Rightarrow5x+y=180\)
\(\dfrac{x}{3}=\dfrac{y}{25}\Rightarrow25x=3y\Rightarrow y=\dfrac{25}{3}x\)
\(\Rightarrow5x+\dfrac{25}{3}x=180\)
\(\Rightarrow\dfrac{40}{3}x=180\)
\(\Rightarrow x=180:\dfrac{40}{3}=\dfrac{27}{2}\)
\(\Rightarrow y=\dfrac{27}{2}:3.25=\dfrac{225}{2}\)
\(\Rightarrow z=\dfrac{27}{2}.4=54\)