[tex]\{x,y,z\}i.p.\{2,3,6\}=\ \textgreater \ \frac{x}{\frac{1}{2}}=\frac{y}{\frac{1}{3}}=\frac{z}{\frac{1}{6}}=k=\ \textgreater \ \\
=\ \textgreater \ x=\frac{k}{2},y=\frac{k}{3},z=\frac{k}{6}\\
x+y+z=15\\
\frac{k}{2}+\frac{k}{3}+\frac{k}{6}=15|*6\\
3k+2k+k=90\\
6k=90=\ \textgreater \ k=15\\
x=\frac{15}{2}\\
y=5\\
z=\frac{5}{2}[/tex]