Bob and mark talk about their families. no says he has 3 kids, the product of their ages is 72. he gives another clue: the sum of the ages of his children. mark points out that there is still not enough information to accurately guess. finally, bob says," my youngest child called justice." mark can correctly determine the ages of bob's children. what are the ages?

Given:
There are 3 kids and the product of their ages is 72.
Youngest child has a name Justice. Meaning, they have different ages.

So, in order for us to know the possible ages, we need to factor 72. Let us use prime factorization.

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

So that will be
1 x 2 x 2 x 2 x 3 x 3 = 72

Based on the factors we can assume the following ages:

1 x 8 x 9   = 72
1 x 3 x 24 = 72
2 x 4 x 9   = 72
3 x 4 x 6   = 72
1 x 4 x 18 = 72

The one above shows the possible ages of the three kids.