# Math Help - Roommates

1. ## Roommates

Two women meet after many years. One asks, "how old are youthree daughters?" Answer: "The product of their ages is 36." Question: "But that's not enought information." Answer: "Well, the sum of their ages is the same number as the post office box that we shared at college." Question: "But that's still not enough information." Answer: "the oldest one looks like me. "Statement: "Oh, now I know their ages."

That is the question on the paper and I have no idea what that is about..

2. I can't figure out what information "the oldest one looks like me" is supposed to give, is there a typo?

3. nope typed right from the paper in my lap

4. Originally Posted by t-lee
Two women meet after many years. One asks, "how old are youthree daughters?" Answer: "The product of their ages is 36." Question: "But that's not enought information." Answer: "Well, the sum of their ages is the same number as the post office box that we shared at college." Question: "But that's still not enough information." Answer: "the oldest one looks like me. "Statement: "Oh, now I know their ages."

That is the question on the paper and I have no idea what that is about..
That there is not enough information to determine the ages from the
knowledge that the sum of their ages is the same as the PO box number
means that there are two or more ways that you can find three factors
of 36 that sum to that number. (probably means that the sum is 13).

The last piece of information tells you that the two oldest are not twins
(and hence of the same age). My guess is the ages are 2, 2 and 9 years.

RonL

5. that is what i thought, still not enough information... speculation is the only way to get some answers. I could not think of any way to figure the numbers without having at least one age or most helpful the po box.

that is number theory for ya

6. Originally Posted by t-lee
Two women meet after many years. One asks, "how old are youthree daughters?" Answer: "The product of their ages is 36." Question: "But that's not enought information." Answer: "Well, the sum of their ages is the same number as the post office box that we shared at college." Question: "But that's still not enough information." Answer: "the oldest one looks like me. "Statement: "Oh, now I know their ages."

That is the question on the paper and I have no idea what that is about..
There is enough infromation.
---
The positilities for $(x,y,z)$ are:
Code:
1,1,36   SUM 28
1,2,18   SUM 21
1,3,12   SUM 16
1,4,9     SUM 12
1,6,6     SUM 13
2,2,9     SUM 13
2,3,6     SUM 11
Examine the last statement.
"The oldest one looks like me".
This implies that the oldest exists.
Furthermore, from the second statement,
"The sum of ages is my POX in college" suggests that the woman was aware of the POX number" otherwise she was not able to say,
"Okay, I know there ages".
Thus, since she knew sum she was not able to determine the ages because there was not a unique possibility. In that case the sum was not unique. Thus,
Code:
1,6,6
2,2,9
Note, the statement "The oldest one looks like me" destroys the first possibility. Thus the daughets were
2,2,9

7. Originally Posted by t-lee
that is what i thought, still not enough information... speculation is the only way to get some answers. I could not think of any way to figure the numbers without having at least one age or most helpful the po box.

that is number theory for ya
Sorry - no speculation, there are two ways that the sum of the ages
can be 13 if the product is 36. If you check you will find no other value
of the sum can be made in two ways, so the PO box number must be 13.

The sum 13 can be made if the ages are 1, 6 and 6 or 2, 2 and 9.

That there is an oldest shows that the answer is the latter 2, 2, and 9 years.

When I used the expressions "guess" it is modest understatement, because
I haven't checked that the problem setter has not made an error that
allows multiple solutions.

RonL

8. i don't understand why it has to be a sum of 13. Why won't 1 4 9 work??

9. Originally Posted by t-lee
i don't understand why it has to be a sum of 13. Why won't 1 4 9 work??
Because we NEED the third piece of information to determine the ages. There is only one way to have more than one combination that makes the mailbox number...that the sum is equal to 13. Otherwise the mailbox information is enough to determine the ages.

-Dan