[tex]2x = 3y = 5z = k[/tex]
[tex]x= \frac{k}{2} \\ y = \frac{k}{3} \\ z = \frac{k}{5} [/tex]
[tex]x + y + z = 31[/tex]
[tex] \frac{k}{2} + \frac{k}{3} + \frac{k}{5} = 31[/tex]
15k+10k+6k=31•30
31k=31•30
k=30
[tex]x = \frac{k}{2} = \frac{30}{2} = 15 \\ y = \frac{k}{3} = \frac{30}{3} = 10 \\ z = \frac{k}{5} = \frac{30}{5} = 6[/tex]