Floors and Ceilings

According to my graphing calculator, there is only one solution.

I got a different answer.

$let\;\;r=x+\delta\qquad$   Where x is an integer and     $0\le\delta<1$

then the problems becomes 

$\lfloor r \rfloor + r = 15.5\\ x+x+\delta=15.5\\ $

I will leave you to think about this and to determine for yourself how many solutions that there are.