Expert: Josh - 5/17/2005

Question
if u multiply their ages by mine the product is 2450, if u add their ages together the result would be double your age. how old am i

Answer
Hi Geoffery,

I am slightly confused by the pronouns. When you mention "they", how many people are we talking about? Okay, suppose that there are two people.
The first piece of clue seems to suggest that the product of two people's age (X*Y) and your age (M) is 2450. For this, we can write X*Y*M=2450....[1]

When you add "their" ages (X+Y), the result would be doulbe "my" age (Do you still mean "your" age, M?). If so, (X+Y)=2*M.

We don't have enough information to solve this problem; unless the first reference to "their ages" actually refers to (X+Y).

In this case, we have
(X+Y)*M=2450 ...[2] and
(X+Y)=2M.....[3]
Substituting [3] into [2], we get
2*(M*M)=2450
M=square_root(2450/2)
=square_root(1225)
=35.

I'm glad it works out in the end, despite the confusion.

Cheers.