# Age Word Problem

#### sarlaur

##### New member
Hi folks, not sure if this is the right category or not.
Here is my problem:

If Sara is twice as old as Eileen will be when Gina is as old as Sara is now, who is the oldest, the middle child, and the youngest?

I have deduced that, obviously, Eileen is not the oldest. She is, at some point, half the age of Sara. Gina also cannot be the oldest because of how it is worded: "as old as Eileen WILL BE WHEN Gina is as old as Sara is NOW." So Sara has to be the oldest, right?

I cannot figure out how to determine who is the middle child and who is the youngest.
We know that S = 2E when G = S... So G = 2E at some point too, right?

That makes Gina the middle child, and Eileen the youngest. Do I have this right?

#### Ishuda

##### Elite Member
Hi folks, not sure if this is the right category or not.
Here is my problem:

If Sara is twice as old as Eileen will be when Gina is as old as Sara is now, who is the oldest, the middle child, and the youngest?

I have deduced that, obviously, Eileen is not the oldest. She is, at some point, half the age of Sara. Gina also cannot be the oldest because of how it is worded: "as old as Eileen WILL BE WHEN Gina is as old as Sara is NOW." So Sara has to be the oldest, right?

I cannot figure out how to determine who is the middle child and who is the youngest.
We know that S = 2E when G = S... So G = 2E at some point too, right?

That makes Gina the middle child, and Eileen the youngest. Do I have this right?
I believe you have it correct but you need something a little more concrete than the "So G = 2E at some point too, right?" for us slower people

My reasoning goes something like this
1) "when Gina is as old as Sara is now" implies Gina is younger than Sara since the 'when' implies 'in the future' and if Gina were older than Sara, Gina could never, in the future, (in the world we live in anyway) be as old as Sara is now. Thus
G = S - x
where G represent Gina's age now, S represents Sara's age now and x is positive.
2) Let E be Eileen's age now. Gina will be as old as Sara is now in x years. So in x years Eileen will be E+x years old and Sara is now twice as old as (E+x), i.e.
S = 2 (E + x)
or, since S = G + x,
2 (E+x) = G + x
of
E = (G - x) / 2

Now, since x is positive
S > G > E