The framework of database repairs and consistent answers to queries is a principled approach to managing inconsistent databases. We describe the first system able to compute the consistent answers of general aggregation queries with the COUNT(A), COUNT(*), SUM(A), MIN(A), and MAX(A) operators, and with or without grouping constructs. Our system uses reductions to optimization versions of Boolean satisfiability (SAT) and then leverages powerful SAT solvers. We carry out an extensive set of experiments on both synthetic and real-world data that demonstrate the usefulness and scalability of this approach.