12 boys and n girls made some cupcakes.... How many children made cupcakes?

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PenPaper
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Can you solve this question?
All help is appreciated, many thanks!


12 boys and n girls made some cupcakes. Every child made the same number of cupcakes. The total number of cupcakes made was n^2 + 10n -2. How many children made cupcakes?
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Lemur14
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(Original post by PenPaper)
Can you solve this question?
All help is appreciated, many thanks!


12 boys and n girls made some cupcakes. Every child made the same number of cupcakes. The total number of cupcakes made was n^2 + 10n -2. How many children made cupcakes?
Moved to the Maths forum

So you know the total number of children in terms of n right?
Then choose a variable name (eg. c) for the number of cupcakes each child makes. Use this information to find the total number of cupcakes made in terms of n and c. You can then equate that to the total number of cupcakes made in terms of n and solve to find the total number of cupcakes
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the bear
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(Original post by PenPaper)
Can you solve this question?
All help is appreciated, many thanks!


12 boys and n girls made some cupcakes. Every child made the same number of cupcakes. The total number of cupcakes made was n^2 + 10n -2. How many children made cupcakes?
the number of cupcakes divided by the number of children must be a whole number.

divide n2 + 10n - 2 by n + 12 using long division.

the remainder is a number r.... which means that r/{n + 12} must be a whole number....
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Lemur14
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(Original post by the bear)
the number of cupcakes divided by the number of children must be a whole number.

divide n2 + 10n - 2 by n + 12 using long division.

the remainder is a number r.... which means that r/{n + 12} must be a whole number....
Or that :laugh: Was trying to avoid it since it was in GCSEs and most GCSE students won't have done that but that's an awful lot simpler!
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the bear
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(Original post by Lemur14)
Or that :laugh: Was trying to avoid it since it was in GCSEs and most GCSE students won't have done that but that's an awful lot simpler!
that question is well hard for GCSE :mad:
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(Original post by the bear)
that question is well hard for GCSE :mad:
Yeah, doesn't quite look GCSE level to me :s but that's where it was :dontknow:
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the bear
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(Original post by Lemur14)
Yeah, doesn't quite look GCSE level to me :s but that's where it was :dontknow:
it is on this Senior Maths Challenge paper ( q 8 )

http://furthermaths.org.uk/docs/GroupRegional1617.pdf
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Lemur14
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(Original post by the bear)
it is on this Senior Maths Challenge paper ( q 8 )

http://furthermaths.org.uk/docs/GroupRegional1617.pdf
Ahh right...definitely not GCSE then :laugh:
In which case your method is much better :yep:
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the bear
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(Original post by Lemur14)
Ahh right...definitely not GCSE then :laugh:
In which case your method is much better :yep:
:five:
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PenPaper
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Thank you all for your help!!
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LowIQ
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(Original post by Lemur14)
Moved to the Maths forum

So you know the total number of children in terms of n right?
Then choose a variable name (eg. c) for the number of cupcakes each child makes. Use this information to find the total number of cupcakes made in terms of n and c. You can then equate that to the total number of cupcakes made in terms of n and solve to find the total number of cupcakes
I got the total in terms of c and n as cn+12c but how would you solve n^2+10n-2=cn+12c
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Lemur14
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(Original post by LowIQ)
I got the total in terms of c and n as cn+12c but how would you solve n^2+10n-2=cn+12c
I think (haven't actually done it admittedly) if you move it over and make it equal to 0 you can solve the quadratic with cs in it. However the approach in post 3 would be much simpler
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(Original post by Lemur14)
I think (haven't actually done it admittedly) if you move it over and make it equal to 0 you can solve the quadratic with cs in it. However the approach in post 3 would be much simpler
Yes I’ve tried post 3 and it was much easier but I’d like to try your method as well
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(Original post by LowIQ)
Yes I’ve tried post 3 and it was much easier but I’d like to try your method as well
It may be wrong (was half asleep when I wrote that tbh) but as I said above equating to 0 and solving as a quadratic seems like the best next step
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(Original post by Lemur14)
I think (haven't actually done it admittedly) if you move it over and make it equal to 0 you can solve the quadratic with cs in it. However the approach in post 3 would be much simpler
Therefore I have n^2+10n-cn-2-12c=0 then how would I factorise this?
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(Original post by LowIQ)
Therefore I have n^2+10n-cn-2-12c=0 then how would I factorise this?
You'll want all the n^2s together then all the ns with their coefficient factored out then the two remaining terms. Not sure if that makes sense sorry...
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(Original post by Lemur14)
You'll want all the n^2s together then all the ns with their coefficient factored out then the two remaining terms. Not sure if that makes sense sorry...
So n^2 +n(10-c)-2(1+6c)=0
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Lemur14
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(Original post by LowIQ)
So n^2 +n(10-c)-2(1+6c)=0
I'd distribute the 2 in the final bracket but yep, now quadratic formula (which I'm praying solves nicely since I haven't tried this)

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PenPaper
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Here's the solution I finally got:
n^2 +10n - 2 / n+12 = n - 2 [r=22]
and you should get a remainder of 22, which equals to n, the number of girls!

wow...

But thank you soooo much for your help!!! @the bear you are correct, this really wasn't gcse, i found that this was actually a question from the UKMT senior maths challenge!
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(Original post by Lemur14)
I'd distribute the 2 in the final bracket but yep, now quadratic formula (which I'm praying solves nicely since I haven't tried this)

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So a is 1, b is (10-c) and c is (1+6c) but that wouldn’t work and if I did a is 1, b is 1 and c is -2 then the answer is 1 and -2 so have I done something wrong?
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