The stacked spectral energy distribution (SED) of Multiband Imaging Photometer for Spitzer (MIPS) 24$\mu m$ detected Lyman break galaxies (MIPS-LBGs) is fitted by means of spectro-photometric model GRASIL with an "educated" fitting approach which benefits from results of chemical evolution models. The star formation rate(SFR)-age-metallicity degeneracies of SED modelling are broken by using SFH and chemical enrichment history suggested by chemical models, which also provide dust mass, dust abundance and chemical elements locked in dust component. We derive the total mass $M_{tot}$, stellar mass $M_{\ast}$, gas mass $M_{g}$, dust mass $M_{d}$, age and SFR of the stacked MIPS-LBG in a self-consistent way. Our estimate of $M_{\ast}= 8\times 10^{10}$ agrees with other works based on UV-optical SED fitting. We suggest that MIPS-LBGs at $z\sim3$ are young (0.3-0.6 Gyr), massive ($M_{tot} \sim 10^{11} M_{\odot}$), dusty ($M_{d} \sim 10^{8} M_{\odot}$), metal rich ($Z \sim Z_{\odot} $) progenitors of elliptical galaxies suffering a strong burst of star formation (SFR $\sim 200 M_{\odot}/yr$). Our estimate of $M_{d}=7 \times 10^{7} M_{\odot}$ of the stacked MIPS-LBG is about a factor of eight lower than the estimated value based on single temperature grey-body fitting, suggesting that self-consistent SED models are needed to estimate dust mass. By comparing with the Milky Way molecular cloud and dust properties, we suggest that denser and dustier environments and flatter dust size distribution are likely in high redshift massive star forming galaxies. These dust properties, as well as the different types of SFHs, can cause different SED shapes between high redshift star-forming ellipticals and local star-burst templates. This discrepancy of SED shapes could in turn explain the non detection at submillimeter wavelengths, of IR luminous ($L_{IR} \succeq 10^{12} L_{\odot} $) MIPS-LBGs.

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