Avery has twelve slips of paper which she wants to put into five cups labeled $P,Q,R,S,T$. She wants the sum of the numbers on the slips in each cup to be an integer. Furthermore, she wants the five integers to be consecutive and increasing from $P$ to $T$. The numbers on the papers are $2,2,2,2,3,3,3,3,3,3.5,4,$ and $4.5$. If a slip with 2 goes into cup $T$ and a slip with 3 goes into cup $Q$, what is the sum of the numbers on the slips in cup $S$?