On July $1,2024,$ Truman Company acquired a $70$ percent interest in Atlanta Company in exchange for consideration of $$804,875$ in cash and equity securities$.$ The remaining $30$ percent of Atlanta's shares traded closely near an average price that totaled $$326,375$ both before and after Truman's acquisition.

In reviewing its acquisition, Truman assigned a $$124,500$ 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.

$\backslash$table$[[$Items$,$Truman,At lanta$],[$Revenues$,,$$ $(780,165),,$$ $(491,000)],[$Operating expenses,,$468,000,,298,000],[$Income of subsidiary,,$(58,835),,0],[$Net income,,$ $(371,000),,$$ $(193,000)],[$Retained earnings, $1/1/24,,$$ $(871,000),,$$ $(534,000)],[$Net income $($above$),,(371,000),,(193,000)],[$Dividends declared,,$150,000,,50,000],[$Retained earnings, $12/31/24,$$$,(1,092,000),,$$ $(677,000)],[$Current assets,,$ $452,790,,$$ $448,000],[$Investment in Atlanta,,$846,210,,0],[$Land$,,458,000,,237,000],[$Buildings$,,748,000,,674,000],[$Total assets,,$ $2,505,000,,$$ $1,359,000],[$Liabilities$,,$$ $(913,000),,$$ $(362,000)],[$Common stock,,$(95,000),,(300,000)],[$Additional paid$-$in capital,,$(405,000),,(20,000)],[$Retained earnings, $12/31/24,,(1,092,000),,(677,000)],[$Total liabilities and stockholders' equity,$$,(2,505,000),$$$,(1,359,000)]]$

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.