By treating the notion of problem as binary correspondence, we provide a simple and adequate formalization for the main components of problems, their basic properties, and constructions. In particular, we arrive at natural formal notions of inverse problem and composition of problems. As an illustration, the inverse problem is considered to a singularly perturbed system of ordinary differential equations which describe a process in chemical kinetics and burning. The inverse problem is corrected and made more practical by means of composition with a simple auxiliary problem which represents the relation between functions and finite sets of numers. For the corrected inverse problem, formulas for the solution are presented and the conditions of unique solvability are indicated.