In this paper, we present a new power allocation scheme for a decode-and-forward (DF) relaying-enhanced cooperative wireless system. While both source and relay nodes may have limited traditional brown power supply or fixed green energy storage, the hybrid source node can also draw power from the surrounding radio frequency (RF) signals. In particular, we assume a deterministic RF energy harvesting (EH) model under which the signals transmitted by the relay serve as the renewable energy source for the source node. The amount of harvested energy is known for a given transmission power of the forwarding signal and channel condition between the source and relay nodes. To maximize the overall throughput while meeting the constraints imposed by the non-sustainable energy sources and the renewable energy source, an optimization problem is formulated and solved. Based on different harvesting efficiency and channel condition, closed form solutions are derived to obtain the optimal source and relay power allocation jointly. It is shown that instead of demanding high on-grid power supply or high green energy availability, the system can achieve compatible or higher throughput by utilizing the harvested energy.