The aim of this talk is the study of an Adjunction-like formula for curves on the weighted projective plane and show how this formula provides a way to compute the cardinal of $\Delta$, for $$ \Delta:=\{ (i,j,k)\in \mathbb{N}^3|\ ai+bj+ck=t\} $$ with $a,b,c,t \in \mathbb{N}$, by means of a certain curve of an appropiate degree in a particular weighted projective plane.