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Old 2005-12-29, 22:47   #1
akruppa
 
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"Nancy"
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Default A text problem

Adam has a sister, Barbara. She is as old as he was when she was half as old as he is. Adam is 24, how old is Barbara?

Alex
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Old 2005-12-29, 23:38   #2
Wacky
 
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Default Then and Now

Quote:
Originally Posted by akruppa
Adam has a sister, Barbara. She is as old as he was when she was half as old as he is. Adam is 24, how old is Barbara?

Alex
The hard part is to parse the English! I take it to mean "was half as old as he is" (now).

To make it more interesting, also try the similar problem that states "was half as old as he was" (then).

She is "of age" (18 in this jurisdiction). In my proposed alternate,
She is a sweet 16.
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Old 2005-12-29, 23:38   #3
tom11784
 
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16
darn Wacky beating me by under a minute

Last fiddled with by tom11784 on 2005-12-29 at 23:39
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Old 2005-12-29, 23:41   #4
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Barbara's brother, Adam, was present when she fell in the well. Why didn't he help her out?
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Old 2005-12-29, 23:45   #5
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He fell in as well
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Old 2005-12-30, 00:26   #6
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Tom,

I'm adverse to verse,
but it will get worse.

As for the age,
we're on a different page.

In the case of the well,
your answer is swell.

A different solution I seek,
(when found, others may reek).

But an English pun,
is really the fun.

So bring in the New Year,
with merriment and Cheer^h^h^h^h^h

Oxydol ?

Happy New Year, Y'all.

Last fiddled with by Wacky on 2005-12-30 at 00:33
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Old 2005-12-30, 09:55   #7
Numbers
 
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Let Barbara's age now be x.
Then 24-x = x - 12.
and so x = 18.

As for why he didn't help her out of the well; she fell in the stair well and picked herself up without his help.
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Old 2005-12-30, 10:07   #8
akruppa
 
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18 is, of course, correct and quite easily verified. I thought the problem was interesting because I found it very hard to wrap my mind around that second sentence! It's not really a complicated sentence and the math is trivial, but for some reason this problem is surprisingly hard to get a grip on (to me anyway).

Alex
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Old 2005-12-30, 10:34   #9
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I know exactly what you mean. I find word problems difficult, period. I always seem to end up with about five variables and to lose track of the essential point of the question.
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Old 2005-12-30, 12:44   #10
Wacky
 
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Quote:
Originally Posted by Wacky
A different solution I seek,
(when found, others may reek).

But an English pun,
is really the fun.
Come now. Your proposed answers are too "logical". This is a riddle.
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Old 2005-12-30, 13:32   #11
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"Adam has a sister, Barbara. She is as old as he was when she was half as old as he is. Adam is 24, how old is Barbara?"

At first I read that as saying that they're the same age, but since this is a word problem, I have to reinterpet it.
Her's old age was A/2. A=24 now.
Her age now is what A was when B=A/2.
B1=A1/2
A2=24
B2=A1
Assume that B1, B2, A1, and A2 are all integers from 1 to 24.
If A1 is even then there exists possible values for B1. Eliminate odds.
Try values of B1:
B1=1, A1=2, A2=3 <-- not a solution
B1=2, A1=4, A2=6 <-- not a solution
B1=3, A1=6, A2=9 <-- not a solution
B1=4, A1=8, A2=12 <-- not a solution
B1=5, A1=10, A2=15 <-- not a solution
B1=6, A1=12, A2=18 <-- not a solution
B1=7, A1=14, A2=21 <-- not a solution
B1=8, A1=16, A2=24 <-- solution
Since 24 is even, then B1 has to be even too since 3(any odd)=another odd.
If I was really lazy in going through test values then I'd also observed that A2=3 * B1. That is what everyone else did.
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