In this paper we present a simple analytical model to estimate the throughput performance in IEEE 802.11 WLANs, in which inelastic traffic competes with elastic traffic. In the considered wireless network the inelastic traffic is composed of asymptotic UDP uplink flows, while the elastic traffic consists of multiple persistent TCP uplink and downlink connections. We show that it is not necessary to precisely characterize the steady-state distribution of the network contention level in order to derive the throughput performance, because the overall TCP traffic can be equivalently modeled as two saturated flows. Starting from this finding, we develop an approximate model to evaluate the throughput of the UDP and TCP connections. Comparison with simulation results demonstrates that our approximate model is accurate in predicting the TCP and UDP throughput performance over a wide range of network and traffic configurations.