A text problem

akruppa · 2005-12-29, 22:47

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

Wacky · 2005-12-29, 23:38

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.

tom11784 · 2005-12-29, 23:38

16
darn Wacky beating me by under a minute

Wacky · 2005-12-29, 23:41

Barbara's brother, Adam, was present when she fell in the well. Why didn't he help her out?

tom11784 · 2005-12-29, 23:45

He fell in as well

Wacky · 2005-12-30, 00:26

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.

Numbers · 2005-12-30, 09:55

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.

akruppa · 2005-12-30, 10:07

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

Numbers · 2005-12-30, 10:34

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.

Wacky · 2005-12-30, 12:44

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.

nibble4bits · 2005-12-30, 13:32

"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.

2005-12-29, 22:47	#1
akruppa "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

2005-12-29, 23:38	#3
tom11784 Aug 2003 Upstate NY, USA 506₈ Posts	16 darn Wacky beating me by under a minute Last fiddled with by tom11784 on 2005-12-29 at 23:39

2005-12-30, 00:26	#6
Wacky Jun 2003 The Texas Hill Country 3²×11² 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 2005-12-30 at 00:33

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2005-12-29, 23:41	#4
Wacky Jun 2003 The Texas Hill Country 1089₁₀ Posts	Barbara's brother, Adam, was present when she fell in the well. Why didn't he help her out?

2005-12-29, 23:45	#5
tom11784 Aug 2003 Upstate NY, USA 2·163 Posts	He fell in as well

2005-12-30, 09:55	#7
Numbers Jun 2005 Near Beetlegeuse 2²·97 Posts	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.

2005-12-30, 10:07	#8
akruppa "Nancy" Aug 2002 Alexandria 100110100011₂ 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

2005-12-30, 10:34	#9
Numbers Jun 2005 Near Beetlegeuse 2²·97 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.

2005-12-30, 13:32	#11
nibble4bits Nov 2005 B6₁₆ 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.