[tex]x+y+z=100 \\ \frac{x}{1} = \frac{y}{3} = \frac{z}{4} = \frac{x+y+z}{1+3+4} = \frac{100}{8} = \frac{25}{2} \\ x= \frac{25}{2} \\ y= \frac{3 \cdot 25}{2} = \frac{75}{2} \\ z= \frac{4 \cdot 25}{2} = \frac{100}{2} =50 \\ \Rightarrow \boxed{\bold{100= \frac{25}{2} + \frac{100}{2} +50}}[/tex]
