$$x:y:z=3:4:5$$

$$x=3k, y=4k, z=5k$$

$$x+y+z=468$$

$$3k+4k+5k=468$$

$$12k=468$$

$$k=\frac{468 }{12}$$

$$k=39$$

$$x=3·39, y=4·39, z=5·39$$

$$x=117, y=156, z=195$$