In the solar wind, Langmuir turbulence can generate electromagnetic waves at the fundamental plasma frequency omega _p . This process can likely result from either linear wave transformations on the ambient random density inhomogeneities or resonant three-wave interactions involving Langmuir waves and ion acoustic oscillations. In the presence of sufficiently intense plasma density fluctuations of scales much larger than the Langmuir wavelengths, the first mechanism may be more efficient than the second one. A new approach to calculate the electromagnetic wave emissions by Langmuir wave turbulence in plasmas with background density fluctuations is developed. The evolution of the Langmuir turbulence is studied by numerically solving the Zakharov equations in such a two-dimensional plasma. The dynamics of the spatial distributions of the electric currents with frequencies close to omega _p is calculated, as well as their emission into electromagnetic waves. The efficiency of this radiation is determined as a function of the level of the Langmuir turbulence, the characteristics of the density fluctuations, the background plasma temperature, the position of the satellite receiver, and the durations of the source's emissions and spacecraft's observations. The results obtained by the theoretical modeling and numerical simulations are successfully compared with space observations of electromagnetic waves radiated during Type III solar radio bursts.