The use of flash-based solid state drives (SSDs) in storage systems is growing. Adding SSDs to a storage system not only raises the question of how to manage the SSDs, but also raises the question of whether current buffer pool algorithms will still work effectively. We are interested in the use of hybrid storage systems, consisting of SSDs and hard disk drives (HDDs), for database management. We present cost-aware replacement algorithms, which are aware of the difference in performance between SSDs and HDDs, for both the DBMS buffer pool and the SSDs. In hybrid storage systems, the physical access pattern to the SSDs depends on the management of the DBMS buffer pool. We studied the impact of buffer pool caching policies on SSD access patterns. Based on these studies, we designed a cost-adjusted caching policy to effectively manage the SSD. We implemented these algorithms in MySQL's InnoDB storage engine and used the TPC-C workload to demonstrate that these cost-aware algorithms outperform previous algorithms.