For any real number x , let [x] denotes the integer part of x ;\ x\...

For any real number $x$, let $[x]$ denotes the integer part of $x ;\{x\}$ be the fractional part of $x (\{x\}=x-|x|)$. Let $A$ denote the set of all real numbers $x$ satisfying $\{x\}=\frac{x+[x]+[x+(1 / 2)]}{20}$ If $S$ is the sum of all numbers in $A$, find $[S]$