Research has deeply investigated several issues related to the use of integrity constraints on relational databases. In particular, a great deal of attention has been devoted to the problem of extracting "reliable" information from databases containing pieces of information inconsistent with regard to some integrity constraints. In this manuscript, the problem of extracting consistent information from relational databases violating integrity constraints on numerical data is addressed. Aggregate constraints defined as linear inequalities on aggregate-sum queries on input data are considered. The notion of repair as consistent set of updates at attribute-value level is exploited, and the characterization of several data-complexity issues related to repairing data and computing consistent query answers is provided. Moreover, a method for computing "reasonable" repairs of inconsistent numerical databases is introduced, for a restricted but expressive class of aggregate constraints. An extension of this method for dealing with the data repairing problem in the presence of weak aggregate constraints which are expected to be satisfied, but not required to, is presented. Furthermore, a technique for computing consistent answers of aggregate queries in the presence of a wide form of aggregate constraints is provided. Finally, extensions of the framework as well as several open problems are discussed.