Suppose that at $370$ K pure solid A is in equilibrium with a liquid solution containing $60$ mol$\%$ A and $40$ mol $\%$ B$.$ Use this information and the Margules equation, estimate the composition of the A and B liquid mixture when it is in equilibrium with pure solid B at the same temperature. The melting temperature and the heat of fusion for solid A and B are: A: $400$K and $3000$ cal$/$mol $,$ B: $390$K and $2800$ cal$/$mol$.$