Final answer:
Mr. D is 45 years old and Mr. F is 36 years old.
Step-by-step explanation:
To solve this problem, let's first assign variables to the ages of Mr. D and Mr. F. Let's say Mr. D's age is 'D' and Mr. F's age is 'F'.
According to the information given, Mr. D is 9 years older than Mr. F. We can represent this as D = F + 9.
Their ages combined is 81, so we can also represent this as D + F = 81.
Now, we can substitute the value of D from the first equation into the second equation: (F + 9) + F = 81. Simplifying this equation gives us 2F + 9 = 81. Subtracting 9 from both sides, we get 2F = 72. Finally, dividing both sides by 2, we find that F = 36.
Substituting the value of F into the first equation, we can find D: D = 36 + 9, which gives us D = 45.
Therefore, Mr. D is 45 years old and Mr. F is 36 years old.