Nephew Needs Help Please.

[kuiperbelt]

A year head teacher wants to put together some 'goody bags' to give out to pupils who have gone the extra mile. She purchases the following:

3 tins of Quality Street, each tin contains 124 items of confectionary.
2 boxes of Milk Tray, each box has 78 items of chocholate.
212 assorted Harry Potter Stickers.

The teacher will distribute evenly all items so that each goody bag contains exactly the same amount of QSt confectionary items, Milk Tray chocolates and HP stickers.

How many goody bags does the teacher need??

[Prudie]

If these numbers are correct I can only assume there will be some QS and Milk tray left. If you split each total of items:
372 QS
156 Milk tray chocs
212 HP stickers
Into their factors you find the stickers number, 212 can only be
2x2x53
53 is prime so can't be split any further so logic would suggest 53 bags with 2 of each item in (as there's not enough Milk tray to put 4 in each bag)

Or I have completely misunderstood the question..

[Buenchico]

Factorising . . .

372 = 31 x 3 x 2^2 (where 2^2 means 2 squared)
156 = 13 x 3 x 2^2
212 =53 x 2^2

So the teacher can have 1, 2 or 4 goody bags. It's not possible to have any other number, as 31, 13 and 53 are prime numbers and so can't be divided up.

[Old_Geezer]

Surely just the one bag containing 372 qs, 156 mt, and 212 hps ? One lucky pupil then.

[Prudie]

I think each bag has to have the same number of the 3 different items in.

[Old_Geezer]

Not as I read it. Just each goody bag should have the same.

[roadman]

It depends how many students have gone the extra mile if only one student has gone the extra mile then they would receive all of the above so they are assuming that you will assume that they are asking to evenly distribute the above into piles of as small quantities as possible but i was always told to read the question and if this is a science question then how better to answer it with another question how many pupils went the extra mile please

[Old_Geezer]

Oh, depends how one interprets your post.

This is confusing. The problem should be clearer.

[Prudie]

You may well be right. No wonder some kids continue to hate maths :-)

[ClareTG0ld]

My reading was that each bag has to have x Quality Streets, y chocs, and z fanfic stickers, where x y and z need not be different. But since, as you pointed out, the prime factors are not exactly brilliant, then the best you could do by this count would be four bags of x = 93, y = 39, z = 53. Which... well I guess it would solve the problem, but in practice seems way too much chocolate.

[gingejbee]

...I do hope this same teacher said "number" of items, and not "amount" of items!

[ClareTG0ld]

need not be identical, that should read.

Maths questions are fine, really -- it's wording them in English that's the problem! And, of course, why the answers have to be so implausible. Far better to, I guess... not distribute all of the items? If she kept a few for herself then you could do, say, 30 bags with 7 stickers each, 5 milk trays, and 12 quality streets, and then the rest could be for small goodies for answering questions one lesson.

[Gizmonster]

If you don't mind left overs, then a quick reckon up with minimal "waste" to give you more bags:
23 bags containing:
16 Quality Street
6 Milk Tray
9 Harry Potter Stickers

This will leave:
4 Quality Street
18 Milk Tray
5 Harry Potter Stickers.

Can anyone improve on this??

[New Judge]

Except the question states "The teacher will distribute evenly all items..." so left overs should not be acceptable. These leaves 1, 2 or 4 bags as the only possible answers (unless you start breaking up individual sweets).

[1581960]

First paragraph - " some 'goody bags' "
singular would not comply, must be 2 or 4 goody bags.

[Prudie]

She can't have very high expectations as head of a whole year and won't plan to have more than 4 pupils who've gone the extra mile.

[kuiperbelt]

jingejbee \I do hope this same teacher said "number" of items, and not "amount" of items!\

That was me paraphrasing. Now I am embarrassed!! Thanx for pointing it out though!!

The times I have complained to my wife about those supermarket signs that allow you to use the 'fast track' lane if you have "5 Items or Less (fewer)" LOL

[kuiperbelt]

Purdue \think each bag has to have the same number of the 3 different items in\

Correct :-)

[kuiperbelt]

Purdue should be Prudie. Sorry Prudie, don't know what happened there LOL

[kuiperbelt]

ClareT \four bags of x = 93, y = 39, z = 53.\

Correct also :-)

[kuiperbelt]

The answer is 4. Nephew likes Buenchico's solution since this is reduced to prime numbers which is what was expected in determining the answer!!