20051229, 22:47  #1 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
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 
20051229, 23:38  #2  
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
Then and Now
Quote:
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. 

20051229, 23:38  #3 
Aug 2003
Upstate NY, USA
2×163 Posts 
16
darn Wacky beating me by under a minute Last fiddled with by tom11784 on 20051229 at 23:39 
20051229, 23:41  #4 
Jun 2003
The Texas Hill Country
441_{16} Posts 
Barbara's brother, Adam, was present when she fell in the well. Why didn't he help her out?

20051229, 23:45  #5 
Aug 2003
Upstate NY, USA
2×163 Posts 
He fell in as well

20051230, 00:26  #6 
Jun 2003
The Texas Hill Country
10001000001_{2} Posts 
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 20051230 at 00:33 
20051230, 09:55  #7 
Jun 2005
Near Beetlegeuse
2^{2}·97 Posts 
Let Barbara's age now be x.
Then 24x = 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. 
20051230, 10:07  #8 
"Nancy"
Aug 2002
Alexandria
4643_{8} Posts 
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 
20051230, 10:34  #9 
Jun 2005
Near Beetlegeuse
110000100_{2} Posts 
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.

20051230, 12:44  #10  
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
Quote:


20051230, 13:32  #11 
Nov 2005
2×7×13 Posts 
"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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