The Struter Partnership has total partners' equity of $$440,000,$ which is made up of Main, Capital, $$308,000,$ and Frist, Capital, $$132,000.$ The partners share net income and loss in a ratio of $80\%$ to Main and $20\%$ 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 $$110,000$ 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 $$145,000$ 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 $$80,000$ for a $20\%$ interest in the equity and a $20\%$ share in any income and loss.