A framework for computing range-consistent answers of aggregate queries in the presence of aggregate constraints is introduced. The range-consistent answer of an aggregate query is the narrowest interval containing all the answers of the query evaluated on every possible repaired database. A wide form of aggregate constraints is considered, consisting of linear inequalities on aggregate-sum functions. In this setting, three types of aggregate queries are investigated, namely
queries. Our approach computes consistent answers by solving Integer Linear Programming (ILP) problem instances, thus enabling well-established techniques for ILP resolution to be exploited.