[tex]x;y;z \ \ \ d.p. \\\\3;4;5 \\\\ \frac{x}{3}=\frac{y}{4}=\frac{z}{5}=k \\\\ x=3k \\ y=4k \\ z=5k \\\\ 2x+3y=69 \\\\ 2*3k+3*4k=69 \\\\ 6k+12k=69 \\\\ 18k=69 \\\\ k=\frac{\not 69}{\not 18}\to \boxed{\frac{23}{6}} \\\\ x=3k=\not 3* \frac{23}{\not 6} \\\\ \boxed{\boxed{x=\frac{23}{2}}} \\\\ y=4k= \not 4 * \frac{23}{\not 6}=2*\frac{23}{3} \\\\ \boxed{\boxed{y=\frac{46}{3}}} \\\\ z=5k=5* \frac{23}{6} \\\\ \boxed{\boxed{z=\frac{115}{6}}} [/tex]
