How do you work this out?

[detective]

A large number of children have had their Christmas lunch at school. 40 kids had mince pies, 50 had Ice Cream and 60 had Christmas cake. Of these number, 11 had mince pies AND Ice cream; 11 had mince pies AND Christmas cake; and 11 had Ice Cream AND Christmas Cake. 9 little gluttons had all THREE. So how many children were there in total?

[country_boy]

I make it 110 if all the others had only one dessert

[Muffet]

150 items of food. 33 ate 2 of them = 66 items. 9 ate 3 of them = 27 items. Total 93 items, so 67 must have had one item only., So 33 + 9 + 67 = 109. (with a bit of luck).

[country_boy]

Correction! - 99 - I didn't read the extra 11

[Muffet]

Correction. 57 had one item only, so total 33+9+57 = 99

[country_boy]

Muffet - 150-67=83, hence you making it 10 more than me

[country_boy]

cross post!
at least we agree on 99!

[factor-fiction]

This is whre those Venn diagrams you did at school come in useful

[factor-fiction]

I think all answers so far are wrong. Answer is 126 isn't it?
27 had mince pies only
37 had ice cream only
47 had cake only
2 had mince pies and ice cream but no cake
2 had mince pies and cake but no icecream
2 had cake and icecream but no mince pies
9 had all three items (cake, mince pie and icecream.
Total 126

Check this answer and it meets all the rules.

Mince pie eaters=27+2+2+9=40

Ice cream eaters = 37+2+2+9=50

Cake eaters = 47+2+2+9=60

Mince pies+ icecream: 2 who had mince pies and icecream but no cake plus 9 who had all three; total11

Mince pies + cake: 2 who had mince pies and cake but no ice cream plus 9 who had all three; total11

Ice cream + cake: 2 who had icecream and cake but no mince pies plus 9 who had all three; total 11

[sohcahtoa]

By drawing a Venn Diagram with 3 intersecting circles. place 9 in the centre, 2 and 2 and 2 in the remaining overlapping sections, and then 27, 47 and 37 in the outermost sections. This all adds up to 126 children.

[factor-fiction]

Yes, definitely 126.
Earlier answers forgot that the 11 who had mince pies and ice cream includes the 9 who had all three items, leaving just 2 who had just mince pies and icecream.
Same logic for the 11 who had pies and cake- of these only 2 had pies and cake but no ice cream.
Same logic for the 11 who had ice cream and cake: this includes 9 who had all three items, leaving just 2 who had icecream and cake without mincepies.
Venn Diagrams are the answer- they're the future!

[THECORBYLOON]

What difference does it make why it's being asked?

[scorpioangel]

i Believe muffet is correct with 99

in answer to Factor

9 had mince pies only - 40 minus 31 - 11 mp & ice cream, 11 mp & cake, and 9 all 3
19 Ice cream only 50 minus 31 - 11 ic & mp, 11 ic & cake, 9 all 3
29 cake only 60 minus 31 - 11 cake & mp, 11 cake & ic, 9 all 3

9 + 19 + 29 = 57
plus 11 + 11 + 11 + 9 = total 99

[cazzle]

With my maths teacher hat on, I would say that if this question were to be set in an exam, the correct answer would be 99 for all the good reasons previously stated.

[factor-fiction]

With my maths teacher hat on I disagree- the answer is 126 not 99.

Please tell me: what's wrong with sohcahtoa's solution?

I think in arriving at 99 you've made an assumption that you can't make: you've assumed all 11 who had mince pies and ice cream didn't have cake- but that's not stated.

[THECORBYLOON]

I've seen a couple of teachers post answers to maths questions that are wrong. If you take the time to draw a Venn diagram, you'll see the answer is 126.

[swannbaker]

You seem to forget little Roger who kept throwing his Brussell sprouts at Sandra , got caught by teacher and was made to stand in the corner with no pudding . So that's 127 .

[podger123]

No answer. This is The Great Fun Quiz which should have been the Title so that we all know where it's from.

[podger123]

To detective, Have you done some detecting and made up YOUR mind? What are you putting? I only got Maths o level at the second attempt and still don't have a clue.
Podge