A man is three times as old as his son and twice as old as his daughter. if the average age of three is 36 1/3 years. how old is the father now?

54 years old

Step-by-step explanation:

First, lets define the man's age.

Let the man be x years old.

The man is 3 times the as old as his son.

Therefore, his son is 1/3 of the man's age.

Then his son must be 1/3 x.

The man is twice as old as his daughter.

Therefore, his daughter is 1/2 of the man's age.

Then his daughter is 1/2 x.

Now, we shall find find their total age in term of the variable x.

Total age = x + 1/3 x + 1/2 x = 11/6 x

We are also given that the average of the three people is 36 1/3 years.

With the average age, we can find the their total age.

Total age = 36 1/3 x 3 = 109/3 x 3 = 109 years.

With these information, we are ready to solve x.

11/6 x = 109

x = 54 years old (nearest year)