A monodisperse polymer sample of molecular weight $10,000 \mathrm{~g} \mathrm{~mol}^{-1}$ is mixed with another monodisperse sample of the same polymer of molecular weight $50,000 \mathrm{~g} \mathrm{~mol}^{-1}$. The total mass of the mixture is $1,000 \mathrm{~g}$ and the total number of moles of the polymer in the mixture is $0.04$ mol. The weight-average molecular weight $\left(\bar{M}_{w}\right)$ of the polymer mixture is __________ $\mathrm{g} \mathrm{mol}^{-1}$ $\text{(rounded off to the nearest integer)}$.
