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Energy-aware routing is an effective way to prolong the lifetime of nodes with scarce battery power in ad hoc networks. The proposed energy-aware routing schemes so far do not consider the energy supply of nodes in route selection. They only consider the residual battery capacity of nodes. This paper proposes energy-aware routing algorithms for ad hoc networks with both battery-powered and mains-powered nodes. The proposed algorithms direct the traffic load to mains-powered nodes to avoid using battery-powered nodes as relay. By tuning some tunable coefficients, these algorithms can provide a trade-off between the operational lifetime of the network and the hop count of the selected routes. We compare the performance of the proposed algorithms with other algorithms which do not differentiate explicitly between mains-powered and battery-powered nodes. We show that when most of the nodes in the network are mains-powered, the use of only the type of power supply of nodes in route selection results in a higher network lifetime compared to using the residual battery capacity of nodes. This implies that in such cases, the routing overhead can be reduced, since there is no need to repeatedly propagate the residual battery capacity of nodes (as needed in so-far proposed energy-aware routing algorithms), while even the network lifetime increases.