[tex]x;y;z \ \ \ \ d.p. \\\\ 10;13;15 \\\\ \frac{x}{10}=\frac{y}{13}=\frac{z}{15}=k \\\\ x=10k \\ y=13k \\ z=15k \\\\ x+z=75 \\\\ 10k+15k=75 \\\\ 25k=75 \\\\ \boxed{k=3} \\\\ x=3*10 \to \boxed{\boxed{30}} \\\\ y=13*3 \to \boxed{\boxed{39}} \\\\ z=3*15 \to \boxed{\boxed{45}}[/tex]
