This work focuses on the evolution of conjoint tumor-normal cells, which undergo chemotherapeutic treatments. The model developed in this work has considered that some of the tumor cells may show resistance to a special type of the chemotherapeutic agent. The drug resistance is considered to be either intrinsic or directly induced by chemotherapeutic drug interaction. Under a series of numerical simulations, the dynamic of the system is studied. The evaluation of this study is based on many factors including, but not limited, to the co-dependency of tumor and normal cells, different treatment strategy in terms of single vs. multiple chemotherapeutic treatments, and the sequence and the time of drug administration. The results provide us with a deeper insight into the factors that their considerations may play a critical role in treatment of cancer progression when the drug resistance is present.