Varieties of quantitative algebras, studied by Mardare, Panangaden and Plotkin, can be presented as categories of algebras for enriched monads on the categories \(\textbf{Met}\) (of metric spaces) or \(\textbf{CMet}\) (of complete metric spaces). We solve the open problem of whether the resulting monads are precisely the strongly finitary ones. The solution is negative: the monad corresponding to two \(\varepsilon \) -close binary operations is not strongly finitary. We characterize the monads representing varieties of quantitative algebras as precisely the 1-basic monads which are the weighted colimits of strongly finitary monads. We conclude that strongly finitary endofunctors on \(\textbf{Met}\) are not closed under composition.