[tex]\{x,y,z\} i.p.\{2,3,8\}\Rightarrow \dfrac{x}{\frac{1}{2}}=\dfrac{y}{\frac{1}{3}}=\dfrac{z}{\frac{1}{8}}=k\Rightarrow x=\dfrac{k}{2},y=\dfrac{k}{3},z=\dfrac{k}{8}\\
2x+3y-8z=420\\
2\cdot \dfrac{k}{2}+3\cdot \dfrac{k}{3}-8\cdot \dfrac{k}{8}=420\\
k+k-k=420\\
\boxed{k=420}\\
x=\dfrac{k}{2}\Rightarrow \boxed{x=210}\\
y=\dfrac{k}{3}\Rightarrow \boxed{y=140}\\
z=\dfrac{k}{8}\Rightarrow \boxed{z=\dfrac{105}{2}}[/tex]
