In this paper, the equivalent combined systems of three-heat-source heat pumps are studied. It is pointed out that there may be three combined ways for us to conceive a reversible three-heat-source heat pump as a combined system having a reversible Carnot heat pump driven by a reversible Carnot engine. Whereas for an endoreversible three-heat-source heat pump affected by the heat resistances, there is only one combined way for us to conceive it as a combined system having an endoreversible Carnot heat pump driven by an endoreversible Carnot engine. Then, the fundamental optimum formula of a three-heat-source heat pump is derived simply and directly by using those of two-heat-source cycles. The optimal peformance of an endoreversible three-heat-source heat pump is thus discussed. The inherent relation between the two-and the three-heat-source cycles as well as the fundamental distinction between the reversible and the endoreversible three-heat-source cycles is also revealed. These results may enrich the theory of finite time thermodynamics, and provide some new theoretical bases for the exploitation and application of three-heat-source apparatus such as chemical heat pumps, absorption heat pumps, and so on.