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PostPosted: Sat Dec 15, 2012 9:42 am 
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DS will be sitting the Latymer Upper exam in January. He did one of their sample maths papers yesterday and there is one question which has us all stumped:

'Beryl says to Algernon, "if you give me £3, we'll have the same amount." Algernon says to Beryl, "if you give me £3, I'll have twice as much as you." Both of them are telling the truth. How much does Algernon have?'

If anyone can explain how to do this I'd be really grateful!

Jess


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PostPosted: Sat Dec 15, 2012 1:10 pm 
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In algebra you can make algernon a and beryl b.
A-3=B
A+3=2B
A+3=2(A-3)
A+3=2A-6.
A-2A=-6-3
-A=-9
A=9

B=A-3=9-3=6

Agernon has £9 and Beryl has £6

answer = £9


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PostPosted: Sat Dec 15, 2012 1:25 pm 
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Location: Watford, Herts
The trick is that giving £3 decreases one amount by £3 and increases the other by £3.
Quote:
Beryl says to Algernon, "if you give me £3, we'll have the same amount."

B+3 = A-3,
or equivalently
B = A-6
Quote:
Algernon says to Beryl, "if you give me £3, I'll have twice as much as you."

A+3 = 2*(B-3)

Substituting the first equation for B,
A+3 = 2*(A-6-3) = 2A - 18
<=> A+21= 2A
<=> A = 21
(and thus from the first equation B = 15)


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PostPosted: Sat Dec 15, 2012 1:33 pm 
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Just lost a reply to Pokemon. I can't see how that's right because if A gave £3 to B they wouldn't have the same. And if B gave £3 to A, A wouldn't have double. Would they? Or have I misunderstood?

WP, I'm afraid you've lost me there!! So what are the values for A& B?! Sorry, am being really thick about this one...

And thanks both for replying.

Sorry, just seen you'd put the values in there WP. Thanks.


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PostPosted: Sat Dec 15, 2012 1:38 pm 
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Location: Watford, Herts
Trying to do it without algebra:
  • Transferring £3 from Algernon to Beryl will make them the same, so Algernon must have £6 more than Beryl.
  • Transferring £3 from Beryl to Algernon will increase the difference between their amounts to £12, and we're told that will leave Algernon with twice as much as Beryl, so that must mean it would leave Beryl with £12 and Algernon with £24.
  • Thus before any transfer, Beryl must have £15 and Algernon £21.
But these private school exams usually assume basic algebra.


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PostPosted: Sat Dec 15, 2012 1:54 pm 
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Sorry, I misunderstood the questions. :oops: :shock:

WP's answer is right.

A-3=B+3
A+3=2(B-3)

2A=3B-3
A=(3B-3)/2


(3B-3)/2 + 3=2(B-3)

3B-3+6=4B-12
B=15
A=(3X15-3)/2=21

pokemon wrote:
In algebra you can make algernon a and beryl b.
A-3=B
A+3=2B
A+3=2(A-3)
A+3=2A-6.
A-2A=-6-3
-A=-9
A=9

B=A-3=9-3=6

Agernon has £9 and Beryl has £6

answer = £9


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PostPosted: Sat Dec 15, 2012 1:58 pm 
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Yes I think most of them have an algebra question in there somewhere, and DS is usually pretty good at it. We must have had a family mental block, because DH and I were struggling too.

Thanks for the explanation.


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PostPosted: Sun Dec 16, 2012 6:34 pm 
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None of the questions should require algebra to solve them; the intention is that candidates would use a method similar to WP's, or even trial and error, which has the enormous benefit of forcing the pupil to check his or her answer. Given the range of schools that LUS's 11+ candidates come from, it would be pointless to set a question where forming and solving a pair of simultaneous equations was the expected method.


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