Bob and mark talk about their families. bob says he has three kids, the product of their age is 72. he gives another clue: the sum of the ages of his children. mark points out there is still not enough information to accurately guess. finally bob says, my youngest called justice. mark then correctly determine the ages of bobs children. what are the ages.

I have answered this question before. This should be in the Mathematics category. 

Given:
Bob has three kids whose ages has the product of 72. I will only be able to give you a set of 3 numbers to represent the ages. Had the sum of the ages been given, the specific ages would be provided.

I just did a prime factorization of 72.

72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 =   9
  9 ÷ 3 =   3
  3 ÷ 3 =   1

1 x 2 x 2 x 2 x 3 x 3 = 72   ⇒ 2³ x 3²

There are a lot of possible combinations, here are a few.

1 x 8 x   9 = 72      ⇒ 1 + 8 + 9 = 18
1 x 4 x 18 = 72      ⇒ 1 + 4 + 18 = 23
2 x 4 x   9 = 72      ⇒ 2 + 4 + 9 = 15

 

He has good intentions maybe he belives in global warming