Răspuns:
Explicație pas cu pas:
Fie x, y și z cele trei părți.
[tex](x;y;z)\:d.p.\:(0,5;0,(3);0,1(6))\Rightarrow\frac{x}{0,5}=\frac{y}{0,(3)}=\frac{z}{0,1(6)}=k\Rightarrow x=0,5k; y=0,(3)k; z=0,1(6)k\Rightarrow x=\frac{5k}{10};y=\frac{3k}{9};z=\frac{(16-1)k}{90}\Rightarrow x=\frac{k}{2};y=\frac{k}{3};z=\frac{15k}{90}\Rightarrow x=\frac{k}{2};y=\frac{k}{3};z=\frac{k}{6}[/tex]
[tex]x+y+z=2,4\Rightarrow \frac{k}{2}+\frac{k}{3}+\frac{k}{6}=2,4\Rightarrow 3k+2k+k=14,4\Rightarrow 6k=14,4\Rightarrow k=2,4\\x=\frac{k}{2}=\frac{2,4}{2}\Rightarrow \boxed{\bold{x=1,2}}\\y=\frac{k}{3}=\frac{2,4}{3}\Rightarrow \boxed{\bold{y=0,8}}\\z=\frac{k}{6}=\frac{2,4}{6}\Rightarrow \boxed{\bold{z=0,4}}[/tex]
