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

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Thread starter 1 year ago
#1
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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1 year ago
#2
(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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1 year ago
#3
(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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1 year ago
#4
(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 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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1 year ago
#5
(Original post by Lemur14)
Or that 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
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1 year ago
#6
(Original post by the bear)
that question is well hard for GCSE
Yeah, doesn't quite look GCSE level to me :s but that's where it was
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1 year ago
#7
(Original post by Lemur14)
Yeah, doesn't quite look GCSE level to me :s but that's where it was
it is on this Senior Maths Challenge paper ( q 8 )

http://furthermaths.org.uk/docs/GroupRegional1617.pdf
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1 year ago
#8
(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
In which case your method is much better
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1 year ago
#9
(Original post by Lemur14)
Ahh right...definitely not GCSE then
In which case your method is much better
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Thread starter 1 year ago
#10
Thank you all for your help!!
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1 year ago
#11
(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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1 year ago
#12
(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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1 year ago
#13
(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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1 year ago
#14
(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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1 year ago
#15
(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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1 year ago
#16
(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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1 year ago
#17
(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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1 year ago
#18
(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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Thread starter 1 year ago
#19
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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1 year ago
#20
(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)

Posted from TSR Mobile
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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