Question 104170
WRONG ANSWER: (previously posted by a different tutor)
***2,3,12 or 3,4,6
***2*3*12=72
***
***and 3*4*6 = 72
***
***if i knew the house number the answer would be more correct 
***house number could be 17 or 13
*** but what has strawberry ice cream have to do with it?
***if the guest knows the ages  just be cause it is the childs favorite does 
***not answer the question.
***oldest child could be either 6 or 12




THE CORRECT ANSWER:


The problem tells me a few important things.

1.  The numbers we are looking for multiply to 72.

2.  When I add the ages up, there will be two sets of factors that will add to the same number (this is why the person couldn't decide until the last bit of information)

3.  That even though we might have twins (the same age) there IS an oldest child.  This is important.  You will see why in a minute:

Possible ages that multiply to 72, but add to the same number:
3*3*8 and 2*6*6

Notice they both add to 14, and multiply to 72, but only one has a highest value.  The ages of the children, then must be 3, 3, and 8.  The oldest of these children is 8.

The biggest problem people have with this sort of math problem is the idea that we can have "twins" or a factor that appears more than once!!!