We present a model which, for the first time, accounts for nucleation, growth and/or resorption of particles of variable composition in aqueous solutions (AS). Devised for describing the precipitation of binary solid solutions, it yields the time evolution of all ion activities in the AS, together with the particle population characteristics: number, size and composition profile of particles as a function of time and of their time of nucleation. We apply this numerical approach to the prototypical case of (Ba,Sr)CO3 solid solution precipitation.We demonstrate the great sensitivity of the composition profiles and particle sizes to the initial conditions under which the AS is prepared, and thus illustrate the possibility of engineering the particle characteristics into a chosen state. Finally, by comparing the precipitation of two solid solutions (Ba,Sr)CO3 and (Ba,Sr)SO4, we evidence the sensitivity of the particle composition profiles to the ratio of the endmember solubility products, which leads to the formation of core-shell particles in the case of (Ba,Sr)SO4.