Measuring precise planet masses, densities, and orbital dynamics in individual planetary systems is an important pathway toward understanding planet formation. The WASP-47 system has an unusual architecture that invites a complex formation theory. The system includes a hot Jupiter ("b") neighbored by interior ("e") and exterior ("d") sub-Neptunes, and a long-period eccentric giant planet ("c"). We simultaneously modeled the K2 transit times and 118 radial velocities to determine precise masses, densities, and Keplerian orbital elements of the WASP-47 planets. For the transiting inner planetary system, we obtain Me = 9.1 ± 1.0 M_E (rho_e = 7.7 ± 1.3 gcc), Mb = 358 ± 12 M_E (rho_b = 0.88 ± 0.11 gcc), and Md = 13.6 ± 2.0 M_E (rho_d = 1.5 ± 0.3 gcc). Combining RVs and TTVs provides a substantially better estimate of the mass of planet d than obtained with only RVs or TTVs. Planets e and d have high densities for their size, consistent with a history of photo-evaporation and/or formation in a volatile-poor environment. Through our RV and TTV analysis, we find that the planet orbits are profoundly circular: e_e