How many values of $r$ are there such that $\lfloor r \rfloor + r = 15.5?$
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.