The Struter Partnership has total partners' equity of $$660,000,$ which is made up of Main, Capital, $$462,000,$ and Frist, Capital, $$198,000.$ The partners share net income and loss in a ratio of $73\%$ to Main and $27\%$ to Frist. On November $1,$ Adison is admitted to the partnership and given a $20\%$ interest in equity and a $20\%$ share in any income and loss.

Prepare journal entries to record the admission of Adison for a $20\%$ interest in the equity and a $20\%$ share in any income and loss under independent assumption.

$(1)$ Record the admission of Adison with an investment of $$165,000$ for a $20\%$ interest in the equity and a $20\%$ share in any income and loss.

$(2)$ Record the admission of Adison with an investment of $$200,000$ for a $20\%$ interest in the equity and a $20\%$ share in any income and loss.

$(3)$ Record the admission of Adison with an investment of $$135,000$ for a $20\%$ interest in the equity and a $20\%$ share in any income and loss.