SOLUTION: Write a full solution for the following question. At at party you overhear another guest asking the age of the hosts' 3 children. The host tells the guest that the product of

Question 104170: Write a full solution for the following question.

At at party you overhear another guest asking the age of the hosts' 3 children. The host tells the guest that the product of his kids' ages is 72 and the sum of their ages is the same as the guest's house number. Now, the other guest obviously knows her own house number but, after thinking for a bit, she is forced to ask the host for additional information. The host then says that his oldest child likes strawberry ice cream and the other guest is able to say their ages. Even though you don't know the guest's house number, you have enough information.
Assuming that all of the ages are whole numbers (1, 2, 3 not 2 1/2). HOw old is his oldest child?
Answer by Ahmath(7) (Show Source): You can put this solution on YOUR website!
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!!!
RELATED QUESTIONS
To have a party at the sports club, you must pay $50 plus $5 per guest. Write an equation (answered by durga@tutor)

Learning.com bought 117 pizzas at Pizza hut for their party. Each guest ate 1/10 of a... (answered by rfer)

Hello I need some assistance with this one Ta. It is asking me to: Write a full solution (answered by checkley75)

At a restaurant you overhear a Realtor bragging about the $12,000 commission on an 8%... (answered by rfer)

Hi! before I go any further with asking a question, I want to say thank you all for... (answered by solver91311)

At very long hotel in Arnold, MD, there are n rooms located along a very long corridor... (answered by 303795)

In a party 70% of the guest drink coffee, 65% of the guest drink Tea, 27% of guest didnt... (answered by KMST)

Michelle has a party and invites 3 friends., each friend invites 3 other friends . each... (answered by god2012)

the fifth graders at mitzi bond are planning to throw an end of the year party at the... (answered by solver91311)