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A little teaser

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Ahmed | 13:28 Fri 05th Nov 2004 | Quizzes & Puzzles
15 Answers

Sharon is twice as old as Graham was when Sharon was as old as Graham is now.

If Graham is 24, how old is Sharon?

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would that be 36
Question Author
No, it's not 36
32.
Question Author
Correct bernardo. Well done.
How long did it take you to work it out?

It more difficult than it sounds.  This is how I worked it out:



(1) Sh is twice as old as Gr was when Sh was as old as Gr is now

(2) Gr = 24



put (2) into (1) and you get



(3) Sh is twice as old as Gr was when Sh was 24



Let a = Sh now

Let b = Gr now

Let c = Sh then

Let d = Gr then



Therefore

(4) "Sh was as old as Gr is now" means b = c

(5) "Sh is twice as old as Gr was" means a = 2d

(6) constant age difference means that a - b = c - d

(7) Gr is now 24 means that b = c = 24



put (4) into (6) and you get

(8) a - b = b - d



put (5) into (8) and you get

(9) 2d - b = b - d



add d to both sides:

(10) 3d - b = b



add b to both sides:

(11) 3d = 2b



we know that b = 24, so:

3d = 48

d = 16


but b = c so therefore c = 24



constant age difference means that a = 32



So Shirley and Graham are now 32 and 24;

when Shirley was 24 they were 24 and 16.




QED

 

 

shame on me. I misread the question.
About 2 or 3 minutes I think.  At first I thought it was easy and straightforward, but I had to resort to algebra instead of instinct.  It took 8 minutes to type out the explanation, and then I had to get rid of loads of coloured bits because the thingy said it was more than 2000 characters.  The gremlin has put in lots of extra spaces.
but who is Shirley ?
Question Author

Well done bernardo.


But you forgot one thing...........The fomulae to change Sharon into Shirley ;-)

It more difficult than it sounds.  This is how I worked it out:


(1) Sh is twice as old as Gr was when Sh was as old as Gr is now
(2) Gr = 24

put (2) into (1) and you get
(3) Sh is twice as old as Gr was when Sh was 24

Let a = Sh now
Let b = Gr now
Let c = Sh then
Let d = Gr then

Therefore
(4) "Sh was as old as Gr is now" means b = c
(5) "Sh is twice as old as Gr was" means a = 2d
(6) constant age difference means that a - b = c - d
(7) Gr is now 24 means that b = c = 24

put (4) into (6) and you get
(8) a - b = b - d


put (5) into (8) and you get
(9) 2d - b = b - d

add d to both sides:
(10) 3d - b = b

add b to both sides:
(11) 3d = 2b

we know that b = 24, so:

3d = 48
d = 16

but b = c so therefore c = 24

constant age difference means that a = 32

So Shirley and Graham are now 32 and 24;
when Shirley was 24 they were 24 and 16.



QED

Shirley is Sharon's twin sister.

Nice one BERNARDO
Before resorting to algebra, I tried out various obvious possibilities like 36, 48, 30, or even 24, but they all didn't work.  So I had to algebra instead.
32
Well done beachy, good work, i am proud of you

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