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

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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?

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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#2

(Original post by

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?

**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?

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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#3

**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?

divide n

^{2}+ 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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#4

(Original post by

the number of cupcakes divided by the number of children must be a whole number.

divide n

the remainder is a number r.... which means that r/{n + 12} must be a whole number....

**the bear**)the number of cupcakes divided by the number of children must be a whole number.

divide n

^{2}+ 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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#5

(Original post by

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!

**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!

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#6

(Original post by

that question is well hard for GCSE

**the bear**)that question is well hard for GCSE

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#7

(Original post by

Yeah, doesn't quite look GCSE level to me :s but that's where it was

**Lemur14**)Yeah, doesn't quite look GCSE level to me :s but that's where it was

http://furthermaths.org.uk/docs/GroupRegional1617.pdf

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#8

(Original post by

it is on this Senior Maths Challenge paper ( q 8 )

http://furthermaths.org.uk/docs/GroupRegional1617.pdf

**the bear**)it is on this Senior Maths Challenge paper ( q 8 )

http://furthermaths.org.uk/docs/GroupRegional1617.pdf

In which case your method is much better

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#9

**Lemur14**)

Ahh right...definitely not GCSE then

In which case your method is much better

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#11

(Original post by

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

**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

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#12

(Original post by

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

**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

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#13

(Original post by

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

**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

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#14

(Original post by

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

**LowIQ**)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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#15

**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

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#16

(Original post by

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

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

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#17

(Original post by

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...

**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...

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#18

(Original post by

So n^2 +n(10-c)-2(1+6c)=0

**LowIQ**)So n^2 +n(10-c)-2(1+6c)=0

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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!

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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#20

(Original post by

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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**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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