[tex]\{x,y,z\} i.p.\{2,3,4\}\Rightarrow \dfrac{x}{\frac{1}{2}}=\dfrac{y}{\frac{1}{3}}=\dfrac{z}{\frac{1}{4}}=k\Rightarrow x=\dfrac{k}{2},y=\dfrac{k}{3},z=\dfrac{k}{4}\\
x+y+z=13\\
\dfrac{k}{2}+\dfrac{k}{3}+\dfrac{k}{4}=13|\cdot 12\\
6k+4k+3k=13\cdot 12\\
13k=13\cdot 12\Rightarrow \boxed{k=12}\\
x=\dfrac{k}{2}\Rightarrow \boxed{x=6}\\
y=\dfrac{k}{3}\Rightarrow \boxed{y=4}\\
z=\dfrac{k}{4}\Rightarrow \boxed{z=3}[/tex]
