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A great deal of ecological theory is based on simple Lotka-Volterra-type of unstructured population models in the study of complex population dynamics and communities. The main reason is to obtain important information for predicting their future evolution. In these unstructured models, it is assumed that all individuals in the population are identical, with the same birth and death rates, and consume equally from shared resources in a homogeneous environment. In reality, these assumptions are not biologically true but still forms a basis for modeling population ecology. We apply this paradigm on the grazing system consisting of coupled ordinary differential equations describing the dynamics of forage resource and livestock population in a grassland ecosystem. We do this by investigating the dynamics of the individuals at different life-history stages of juvenile and adult livestock. The mathematical derivation of the model is carried out to show how the physiologically structured population model can be approximated using a three stage-structured population model. Thus the resulting system of ordinary differential equations can be solved to predict density-dependent properties of the population since it provides a somewhat close-to-reality description of the natural and traditional grazing system. This model therefore certainly contains the needed information in the modeling methodology and accommodates the necessary amount of biological details about the population.