A$,$ B and C have a successful partnership. Prior to the admission of D as a partner, the capital account balances for A$,$ B and C are $$540,000,$ $$900,000$ and $$360,000,$ respectively. The profit and loss ratios are $30\%$ to A$,50\%$ to B and $20\%$ to C$.$ D pays $$600,000$ directly to the partners to acquire a $30\%$ ownership interest in the partnership.

a$.$ Prepare the entry to record the admission of Partner D using the goodwill method.

b$.$ What are the profit and loss ratios to the partners after the admission of D$?$