We have performed a sub-meV photoemission study on Mg(B1−xCx)2 for x = 0–0.075. The superconducting (SC) transition temperature (Tc) changes systematically from 38 K to 24 K with increasing the carbon concentration. Because of the extremely high-energy resolution of sub-meV, two features corresponding to the two SC gaps originated from π and σ bands are clearly observed even in raw spectra up to x = 0.075. From numerical analyses, we found that the gap size of the σ band is proportional to Tc, while that of the π band is almost constant. The temperature and carbon concentration dependences of the two gaps are explained within a simple two-band model based on a mean field theory. Using the theoretical model, we deduced interband and intraband coupling strength constants. The transition temperature is dominated by the intraband coupling of the σ band, while the interband coupling slightly increases with increasing the carbon concentration. The two-band model shows that the interband coupling slightly pushes up Tc.