In order to enable low-latency computation-intensive applications for mobile user equipments (UEs), computation offloading becomes critical necessary. We tackle the computation offloading problem in a mixed fog and cloud computing system, which is composed of an long term evolution-advanced (LTE-A) small-cell based fog node, a powerful cloud center, and a group of UEs. The optimization problem is formulated into a mixed-integer non-linear programming problem, and through a joint optimization of offloading decision making, computation resource allocation, resource block (RB) assignment, and power distribution, the maximum delay among all the UEs is minimized. Due to its mixed combinatory, we propose a low-complexity iterative suboptimal algorithm called BTFA based joint computation offloading and resource allocation algorithm (FAJORA) to solve it. In FAJORA, first, offloading decisions are obtained via binary tailored fireworks algorithm; then computation resources are allocated by bisection algorithm. Limited by the uplink LTE-A constraints, we allocate feasible RB patterns instead of RBs, and then distribute transmit power among the RBs of each pattern, where Lagrangian dual decomposition is adopted. Since one UE may be allocated with multiple feasible patterns, we propose a novel heuristic algorithm for each UE to extract the optimal pattern from its allocated patterns. Simulation results verify the convergence of the proposed iterative algorithms, and exhibit significant performance gains could be obtained compared with other algorithms.