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Short-chain alcohols at high dilution are among the very few solutes that enhance the anomalous behavior of water, in particular the value of the temperature of maximum density. This peculiar feature, first discovered experimentally in the early sixties, has remained elusive to a full explanation in terms of atomistic models. In this paper, we first introduce a two-site model of tert-butanol in which the interactions involving hydrogen bonding are represented by a Stillinger-Weber potential, following the ideas first introduced by Molinero and Moore, [J. Phys. Chem. B, 113, 4008, (2009)]. Our model parameters are fit so as to semi-quantitatively reproduce the experimental densities and vaporization enthalpies of previously proposed united atom and all atom OPLS models. Water is represented using the aforementioned potential model introduced by Molinero and Moore, with cross interaction parameters between water and tert-butanol optimized to yield a reasonable description of the experimental excess enthalpies and volumes over the whole composition range of the mixture. We will see that our simple model is able to reproduce the presence of a maximum in the change of the temperature of maximum density for very low alcohol mole fractions, followed by a considerable decrease until the density anomaly itself disappears. We have correlated this behavior with changes in the local structure of water and compared it with the results of all-atom simulations of water/tert-butanol mixtures.