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This paper aims to combine adaptive modulation and coding with layered video coding to improve the quality of video services to users experiencing differing radio conditions, in the context of broadcast and multicast standards such as MBMS and BCMCS. We propose an optimal radio resource allocation algorithm which maximizes a general performance metric for a video session in polynomial time. We show that system-wide optimal resource allocation can be obtained by combining our algorithm with a simple two-step decomposition of the system. In some configurations frequent re-allocations of resource are required, so we also present a sub-optimal allocation algorithm which runs in near linear time. Simulation results show better video quality than existing resource allocation schemes over a range of conditions, and also suggest that the difference between the performance of optimal and suboptimal solutions is less than 3%.