\(\dfrac{x+1}{3}=\dfrac{y+2}{4}=\dfrac{z+3}{5};x+y+z=18\)
\(\Rightarrow\dfrac{x+y+z+\left(1+2+3\right)}{3+4+5}=\dfrac{18+6}{12}=2\)
\(\Rightarrow\dfrac{x+1}{3}=2\)
\(x=2.3-1=5\)
\(\Rightarrow\dfrac{y+2}{4}=2\)
\(=y=2.4-2=6\)
\(\Rightarrow\dfrac{z+3}{5}=2\)
\(z=2.5-3=7\)