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November 26, 2013

How old are John and Julia?

Julia is as old as John will be when Julia is twice as old as John was when Julia's age was half the sum of their present ages. John is as old as Julia was when John was half the age he will be 10 years from now. How old are John and Julia?


Shivraj said...

john: 30
julia: 40.

good one!:)

Matt said...

This is a very tough one. I cannot quite distinguish all of the premises.

Great to have you back blogging!!!

Anonymous said...

Julia John
(Ju + Jo)/2 <==> Jo - Ju/2 + Jo/2
3Jo -Ju <==> -2Ju + 4 Jo = Ju

1) 3Ju = 4Jo

Jo = Ju - Jo/2 + 5 <==> Jo/2 + 5

2) 3/2Jo-Ju = 5

Ju = 40
Jo = 30

Anonymous said...

I needed a lot of baby steps to figure this one out, but I did it! First I made my own typographical representation:
and D=J'':(D''=(D+10)/2)
This exactly corresponds to the sentences as phrased in the riddle. I then realized that I could get rid of the colon relationship by using the simple equation J=x+D. This unchanging difference between their ages would help me negotiate all those past and future ages. In the end I had these four equations that I could easily solve through substitution.
1)D'= (D+J)/2 - x <--These first two were the first typographical string broken up.>
2)J = 2D' - x
3)J = x+D
4)D = (D+10)/2 + x

Anonymous said...

dead by the time i figure it out