On July $1,2024,$ Truman Company acquired a $70$ percent interest in Atlanta Company in exchange for consideration of $$776,000$ in cash and equity securities$.$ The remaining $30$ percent of Atlanta's shares traded closely near an average price that totaled $$314,000$ both before and after Truman's acquisition.

In reviewing its acquisition, Truman assigned a $$140,500$ fair value to a patent recently developed by Atlanta, even though it was not recorded within the financial records of the subsidiary. This patent is anticipated to have a remaining life of five years.

The following financial information is available for these two companies for $2024.$ In addition, the subsidiary's income was earned uniformly throughout the year. The subsidiary declared dividends quarterly.

Required:

a$.$ How did Truman allocate Atlanta's acquisition$-$date fair value to the various assets acquired and liabilities assumed in the combination?

b$.$ How did Truman allocate the goodwill from the acquisition across the controlling and noncontrolling interests?

c$.$ How did Truman derive the Investment in Atlanta account balance at the end of $2024?$

d$.$ Prepare a worksheet to consolidate the financial statements of these two companies as of December $31,2024.$ At year$-$end, there were no intra$-$entity receivables or payables.