A broadcast transmission scheme for multimedia broadcast multicast services (MBMS) is proposed using a coded system with users' feedback in wireless systems. In the proposed transmission scheme, it is possible to adjust the transmission rate with binary users' feedback signals to maximize the overall throughput for a given set of users as a user-ware broadcast transmission scheme. The proposed scheme does not aim at providing reliable transmissions, but maximizing the overall throughput. An adaptive algorithm is proposed to decide the transmission rate adaptively for given channel-user environments using finite-difference stochastic approximation (FDSA). Furthermore, we consider a multi-layer transmission scheme to provide multi-grade MBMS and also derive an adaptive algorithm to adapt multiple transmission rates to given channel-user environments.