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PostPosted: Wed Apr 28, 2010 9:35 pm 
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In class , one third of the pupils bring a teddy bear to school. Last term, each boy took 12 books out of the library, each girl took 17 books and each teddy bear took 9 books. In total 305 books were taken out.

How many girls in class? :cry:


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PostPosted: Wed Apr 28, 2010 9:40 pm 
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I didn't think teddies could read??? - sorry that time of night, brain has ceased to work


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PostPosted: Wed Apr 28, 2010 10:17 pm 
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Is this an 11 plus question or Maths challenge?

I am fairly sure the answer is 7 girls

7 girls - 119 books
11 boys - 132 books

18 children thus 6 teddies taking 54 books.

total 305.


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PostPosted: Wed Apr 28, 2010 10:24 pm 
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Thanks - 11+ question

what is the method (other than trial and error) of arriving at 7 girls and 11 boys -
i understand 1/3 etc from thence :(


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PostPosted: Wed Apr 28, 2010 10:34 pm 
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Sorry - no idea.

I did:

Teddies = 1/3 (Girls+Boys)
305 = 12xboys + 17xGirls + 9xteddies

305 = 12B + 17G + 9x 1/3 (G+B)
305 = 15B + 20 G

then got stuck on the theory so trial and errored from there, remembering that G + B had to be a number devisable by 3.
Hopefully someone with less rusty maths than me can help. :?


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PostPosted: Wed Apr 28, 2010 10:43 pm 
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Location: Finchley - Barnet
13 girls=221 books

remaining 84 between boys and teddies, say 4 boys 4 teddies=4x12+4x9=84

Hence given earlier answers, more than one solutions to the problem

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sj355


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PostPosted: Thu Apr 29, 2010 7:00 am 
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Sorry sj355 but I disagree. You end up with 17 children. A third must have teddies so thats 5 2/3 teddies.

Taking 2/3 of a teddy to school is cruel and if his head is missing he won't be able to read the books anyway!


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PostPosted: Thu Apr 29, 2010 2:09 pm 
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Is there a piece of information missing, like the number of children in the class? I think this might be needed to solve the question.


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PostPosted: Thu Apr 29, 2010 2:37 pm 
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This is a junior maths challenge question.
This is how they answer it:

Number of boys is b
girls = g
teddy bears = 1/3 of b+g
In total boys took out 12b books
girls took out 17g books
total yaken out by bears 9 x 1/3(b+g) = 3(b+g)

So 12b + 17g +3(b+g) = 305
15b + 20g = 305

3b + 4g = 61
There are 5 positive integer solutions of this but...

If 1/3 of b + g is a positive integer, then b = 11 and g=7

This is a diophantine equation.

:shock: :shock: :shock:


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PostPosted: Thu Apr 29, 2010 4:58 pm 
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We need an 'awesome' emoticon.

I'm sure the Herts papers are much easier than that! Having said that, I left the maths to OH. :)


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