Question

Tìm x, y , z :

2x = 3y = 5z và x + y - z = 95

Answer 1

\(2x=3y=5z;\frac{x}{\frac{1}{2}}=\frac{y}{\frac{1}{3}}=\frac{z}{\frac{1}{5}}\)   và \(x+y-z=95\)

Áp dụng tính chất dãy tỉ số bằng nhau :

\(\frac{x}{\frac{1}{2}}=\frac{y}{\frac{1}{3}}=\frac{z}{\frac{1}{5}}=\frac{x+y-z}{\frac{1}{2}+\frac{1}{3}-\frac{1}{5}}=\frac{95}{\frac{19}{30}}=150\)

\(\Rightarrow\)\(\frac{x}{\frac{1}{2}}=150\Rightarrow x=150.\frac{1}{2}=75\)

\(\Rightarrow\)\(\frac{y}{\frac{1}{3}}=150\Rightarrow y=150.\frac{1}{3}=50\)

\(\Rightarrow\)\(\frac{z}{\frac{1}{5}}=150\Rightarrow z=150.\frac{1}{5}=30\)