Salem Company. a subsidiary corporation

Duke Corporation owns a 70 percent equity interest in Salem Company. a subsidiary corporation. During the current year,
a portion of this stock is sold to an outside party. Before recording this transaction, Duke adjusts the book value of its
investment account.
What is the purpose of this adjustment?
How would the parent record the sales transaction?
How would Duke account for the remainder of its investment subsequent to the sale of this partial interest?