On January 12, 2021, Mr. and Mrs. Nixon moved out of their old residence (where they had lived for 22 years) and into a new residence purchased nine days earlier on January 3. They finally sold their old residence on June 7, 2021, for a $278,000 realized gain. 

a. How much gain did they recognize on the sale of their old residence? 

b. On February 26, 2023, Mr. and Mrs. Nixon sold their new residence for a $48,000 realized gain and moved into a nearby house because it had a swimming pool. How much gain would they recognize? 

c. How much gain would they recognize if they sold the new residence because Mrs. Nixon accepted a job in a different state and the family had to relocate?