Hi there,
i am taking auniversity course that deals with teaching math in at the elemenatry level. My prof. has given us a question that I am just stumped about. here is the whole question

An encyclpoedia saleman call at a home. The woman who answers the door says she will buy something from him if he can give the ages of her three children. The first clue, she says, is the three ages multiplied together equal 36. he responds that he needs more infomration, so she says that the threee ages add up to the number of the bus that passed by (the prof did not give us this number) He thinks for a while and says he needs one more clue. So she says, my youngest child has red hair, and he is able to answer and make the sale. what are the ages of the three children? (hint: the salesman needed all three clues to get the answer).

Thanks for your help,
Andrea

Use the fact that the product of the ages is 36 = 2² 3² to write a list of all possible ages for the three daughters. For example they can be

• 1, 1 and 36
• 1, 2 and 18
• etc.

For each, sum the ages to get all possible sums.

• 1, 1 and 36 ---> sum 38
• 1, 2 and 18 ---> sum 21
• etc.

Look at the list of sums. Why is it that knowing which is the correct sum (it is the same as the number on the bus he just saw) is not enough information for the salesman to completely determine the ages? How does the third clue determine the ages?