AT-OEMO-REG 2008 Problem 2

For a real number $x$ is $[x]$ the next smaller integer to $x$ , that is the integer $g$ with $g\leqq<g+1$ , and $\{x\}=x-[x]$ is the "decimal part" of $x$ . Determine all triples $(a,b,c)$ of real numbers, which fulfil the following system of equations: $$\{a\}+[b]+\{c\}=2,9$$$$\{b\}+[c]+\{a\}=5,3$$$$\{c\}+[a]+\{b\}=4,0$$