The compatibility of a given ranking with a dataset consisting of prices, income distributions and total resources is shown to be equivalent to the existence of a solution to a set of linear equalities and inequalities. Their structure makes their solution easier to compute than the solutions of Afriat's inequalities that characterize the rationalizability of a finite set of individual consumption data. Exploiting this structure, we also give new proofs of the rationalizability of finite data sets where total resources are close to being collinear and the contractibility and pathconnectedness of the set that consists of rationalizable finite datasets.