Question of respective ages

[abskebabs]

Here's one I think people may enjoy. I would recommend using pen and paper to solve it.

 

"Keith is twice as old as as Joseph was when Keith was half as old as Joseph will be when Joseph is three times as old as Keith was when Keith was three times as old as Joseph. Their combined ages make forty eight"

 

How old are they?

 

Enjoy:D

[Aeternus]

[hide]Keith is 30 and Joseph is 18.

 

Working Backwards to get equations -

 

"Their combined ages make forty eight."

K + J = 48

"when Keith was three times as old as Joseph"

(K - y) = 3(J - y) for some given y years ago.

"Joseph is three times as old as Keith was when Keith" - Hence 3 x Keiths age in the above equation

3(K-y)

"Keith was half as old as Joseph will be when Joseph is" - So half the above age

3(K-y)/2

"Keith is twice as old as Joseph was when Keith" - So Twice Josephs age from the above equation for Keiths age, so Keiths age minus the difference between them -

K = 2(3(K-y)/2 - (K-J))

 

Now reduce the equation a little

 

K = 3(K-y) - 2(K-J)

K = 3K - 2K -3y -2J

3y = 2J

y = 2J/3

 

So we now have 3 equations in K,J, and y -

 

K + J = 48

(K-y) = 3(J-y)

y = 2J/3

 

So substitute to solve -

 

(K - 2J/3) = 3(J - 2J/3)

K - 2J/3 = 3(J/3)

K - 2J/3 = J

K = 5J/3

 

K + J =48

5J/3 + J = 48

8J/3 = 48

J = 18

 

K = 48 - 18 = 30[/hide]

 

Hopefully that's right

[abskebabs]

Well done my friend, you are correct;) . I must say I'm pleasantly surprised at how quickly an answer was found. I had a very similar method using algebra like you have shown to solve the problem.

 

It would be good if the answers could have been covered up so more people could try this problem. Personally however, I do not know how to do this either.

[timo]

It would be good if the answers could have been covered up so more people could try this problem.

You could try hitting the "report post" option and ask for some moderator to hide the reply with the spoiler tags. Explicit note: That's not what the "report post" option is for, but I suspect the current usage of the option is limited enough so that you don't cause overly much bureocratic trouble.

 

Personally however, I do not know how to do this either.

Often, when you see someone using a feature that you don't know how to use (the spoiler tag is used quite frequently in this very subforum, so just look around for it) you can quote the post and look at the source you get within the quote tags.

EDIT: Not as frequently as I thought; I was fooled by someone using the spoiler tags in his/her signature ;|. Whatever, I found a post using it, quoted it. The code is [ hide] secret message [ /hide] or [hide] secret message [/hide]

[Aeternus]

Well done my friend, you are correct;) . I must say I'm pleasantly surprised at how quickly an answer was found. I had a very similar method using algebra like you have shown to solve the problem.

 

It would be good if the answers could have been covered up so more people could try this problem. Personally however, I do not know how to do this either.

 

Oops, sorry. It completely slipped my mind, it was about 12:30am at the time.

[YT2095]

fixed

[Pre4edgc]

Sorry about that. Do you want me to remove them?

[abskebabs]

Thanks for the help everyone. Pre-edge; what is it you are proposing removing?

[timo]

Probably the signature. No, not really.

[Pre4edgc]

Ok. Just wondering.