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

Original post by PenPaper

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

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 :smile:

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 :smile:

Reply 2

Original post by PenPaper

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

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....

Reply 3

Original post by the bear

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!

Reply 4

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 :mad:

Reply 5

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:

Reply 6

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

Reply 7

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:

Reply 8

Original post by Lemur14

Ahh right...definitely not GCSE then :laugh:

In which case your method is much better :yep:

Reply 9

PenPaper

Thank you all for your help!!

Reply 10

Original post by Lemur14

Moved to the Maths forum :smile:

I got the total in terms of c and n as cn+12c but how would you solve n^2+10n-2=cn+12c

Reply 11

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 :smile:

Reply 12

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 :smile:

Yes I’ve tried post 3 and it was much easier but I’d like to try your method as well

Reply 13

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 :smile:

Reply 14

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 :smile:

Therefore I have n^2+10n-cn-2-12c=0 then how would I factorise this?

Reply 15

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...

Reply 16

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

Reply 17

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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Reply 18

PenPaper

Here's the solution I finally got:
n^2 +10n - 2 / n+12 = n - 2 [r]
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!

Reply 19