\(\frac{x}{y}=\frac{8}{5}\Rightarrow\frac{x}{8}=\frac{y}{5}\Rightarrow\frac{x}{16}=\frac{y}{10}\)
\(\frac{y}{z}=\frac{2}{7}\Rightarrow\frac{y}{2}=\frac{z}{7}\Rightarrow\frac{y}{10}=\frac{z}{35}\)
\(\frac{x}{16}=\frac{y}{10}=\frac{z}{35}=\frac{x+y+z}{16+10+35}=\frac{61}{61}=1\)
x = 16; y = 10; z = 35