[tex] \frac{x}{4} = \frac{y}{7}= \frac{z}{10} =k \\ \\ x=4k; \;\;\;\;\;\;\;y=7k; \;\;\;\;\;\;\; z=10k \\ \\ 2x+3y+z=2*4k+3*7k+10k=156 \\ 8k+21k+10k=156 \\ 39k=156 \\ \\ k= \frac{156}{39} = 4 \\ x=4k=4*4=\boxed{16}\\y=7k = 7*4 =\boxed{28}\\ z=10k= 10*4 = \boxed{40}[/tex]
