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In practice, finite mixture models were often used to fit various type of observed phenomena, specifically those which are random in nature. In this paper, a finite mixture model based on weighted versions of exponential and gamma distribution is considered and studied. Some mathematical properties of the resulting model are discussed including moment generating function, skewness, kurtosis, survival function, hazard rate function, stochastic ordering, order statistics, Bonferroni and Lorenz curves, Renyi entropy measure and estimation of the model parameters. Two real-life data applications from different fields exhibit the fact that in certain situations, the proposed mixture model might be a better alternative than the existing popular models.