floor and ceiling help

First, we note that r must be positive, since otherwise \(\lfloor r \rfloor + r\) is nonpositive. Next, because \(\lfloor r \rfloor + r\) is an integer and \( \lfloor r \rfloor + r=12.2\), the decimal part of r must be 0.5. Therefore, r=n+0.5 for some integer n, so that \(\lfloor r \rfloor + r\) and \(\lfloor r \rfloor + r = 2n+0.5 =16.5\). Therefore, n=8, and the only value of r that satisfies the equation is \(\boxed{r=8.5}\).