The Lagrangian formulation of classical mechanics and its applications figure prominently in the educational literature. Yet systems with variable mass are summarily excluded from this formulation and discussed in terms of Newtonian theory only. This omission is neither technically justified nor desirable from a pedagogical point of view, because it might suggest to the student that such systems are beyond the scope of the Lagrangian approach. Therefore, the authors show that the formalism can be readily extended to include those variable mass systems that are treated in the textbooks in a Newtonian fashion, and its application is illustrated by means of three instructive examples.