\(\frac{3x}{4}=\frac{y}{2}=\frac{3z}{5}\)
\(\Rightarrow\frac{x}{\frac{4}{3}}=\frac{y}{2}=\frac{z}{\frac{5}{3}}=\frac{x+y+z}{5}=\frac{x-z}{-\frac{1}{3}}=\frac{15}{-\frac{1}{3}}=-45\)
\(\Rightarrow x+y+z=-45.5=-225\)
Giải:
Ta có: \(\frac{3x}{4}=\frac{y}{2}=\frac{3z}{5}\Rightarrow\frac{x}{\frac{4}{3}}=\frac{y}{2}=\frac{z}{\frac{5}{3}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x}{\frac{4}{3}}=\frac{y}{2}=\frac{z}{\frac{5}{3}}=\frac{x-z}{\frac{4}{3}-\frac{5}{3}}=\frac{15}{-\frac{1}{3}}=-45\)
+) \(\frac{x}{\frac{4}{3}}=-45\Rightarrow x=-60\)
+) \(\frac{y}{2}=-45\Rightarrow y=-90\)
+) \(\frac{z}{\frac{5}{3}}=-45\Rightarrow z=-75\)
\(\Rightarrow x+y+z=-225\)
Vậy x + y + z = -225