Assignment:
During the census, a man told the census-taker that he had three children. When asked their ages he replied, " The product of their ages is 72. The sum of their ages is my house number." The census taker turned around and ran outside to look at the house number displayed over the door. He then re-entered the house and said, " Using the information you have given me, I cannot tell their ages." The man then said, "I should have told you that the oldest likes angel food cake." Hearing this, the census-taker promptly wrote down the ages of the three children. What did he write?
Provide complete and step by step solution for the question and show calculations and use formulas.