My math teacher asked me this 3 weeks ago and I can't figure it out

Question

Bob and Mark talk about their families. Bob 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 then correctly determine the ages of Bob's children. What are the ages?

Answer 1

72=1*2*2*2*3*3

 

Possible Ages      Sum of The Ages

 

1  2  36                      39

1  4  18                      23

1  8  9                        18

1  3  24                      28

2  3  12                      17

2  4  9                        15

2  6  6                        14

2  2  18                      22

3  3  8                        14

3  4  6                        13

Bob must have said that the sum of the ages of the children is 14. There are two sums that are 14.

The children could be 2, 6, and 6 or the children could be 3, 3, and 8. The third clue says that the youngest child is called Justine. This implies that the two youngest must not be the same age. The youngest must have a distinct age different from the others. This means that the children can't be 3, 3, and 8 because the two youngest would be the same age. The ages must therefore be 2, 6, and 6, making only the youngest having a distinct age of 2. If the sum of the ages was any other sum, 39, 23, 18, 28, 17, 15, 13, or 22, then Mark could have determined the ages without any more clues.

 

Answer 2

PLZ remember that this is a math problem.  The words (story) simply give the math conditions that help us solve the problem.  Read and re-read the problem until you understand it and can put it into your own words.

How’s this?  Bob has 3 kids.  The product of their ages is 72.  There is a youngest.  Knowing the sum of the kid’s ages is not enough information to determine their ages, but knowing that there is a youngest is enough information.

 

The math:

  The prime factors of 72 are 2, 2, 3, 3.

 

  If there are 3 kids and the product of their ages is 72, these are the possible ages:

        2, 2, 9

        2, 3, 6

        3, 3, 4

 

There is a youngest (not twins).  That means the ages are 2, 3, and 6.