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 Post subject: Help pleasePosted: Thu Jan 01, 2015 10:27 pm

Joined: Thu Oct 16, 2014 10:55 am
Posts: 41
can someone help me with this question? I can do it with algebra but my son is finding it hard to understand. If you can do this with some other method please help me

In a group of children two thirds said they enjoyed playing football and three quarters said they enjoyed swimming. If 20 of the group said they enjoyed both activities, what was the total number in the group

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 Post subject: Re: Help pleasePosted: Fri Jan 02, 2015 9:22 am

Joined: Sat Aug 10, 2013 11:46 am
Posts: 188
Draw an overlapping line diagram

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 Post subject: Re: Help pleasePosted: Fri Jan 02, 2015 9:40 am

Joined: Wed Jul 01, 2009 1:04 pm
Posts: 1186
Without further information there isn't a unique answer to this question. At one extreme end of the range you could have the situation where all the children who enjoy football also enjoy swimming (and therefore one quarter like neither). At the other end you could have the situation where all children like one or other sport. Is this the full wording of the question?

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 Post subject: Re: Help pleasePosted: Fri Jan 02, 2015 10:07 am

Joined: Fri Oct 12, 2007 12:42 pm
Posts: 3813
Another great question for bar modelling.

Find the common denominator of quarters and thirds (twelfths).
Draw a long box.
Split it into 12 pieces.
3/4 = 9/12 start at the left of the box and write S in 9 boxes.
2/3 = 8/12 start at the right of the box and write F on 8 boxes.
5 boxes will have F and S. Those are your 20 children. Each box is therefore 4 children.
12 boxes of 4 children each.
48 children.

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 Post subject: Re: Help pleasePosted: Fri Jan 02, 2015 11:05 am

Joined: Wed Jul 01, 2009 1:04 pm
Posts: 1186
But equally all 2/3 (8/12) children who like football, could also like swimming. in which case 8/12 = 20, so the group is 30 children. You are assuming that all children like one or other, which is not stated.

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 Post subject: Re: Help pleasePosted: Fri Jan 02, 2015 11:33 am

Joined: Sun Sep 09, 2012 6:32 pm
Posts: 290
The question tells you that 20 like both activities.

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 Post subject: Re: Help pleasePosted: Fri Jan 02, 2015 11:42 am

Joined: Thu Oct 16, 2014 10:55 am
Posts: 41
Yes, ladymuck, it is a full wording question and answer is 48. Thank you moved,that is what I was looking for.
I did put that information into Venn diagram and by considering total number of children x
We get the equation
2x/3- 20+20+3x/4- 20=x
2x/3+3x/4- 20=x
17x/12-x/1=20
5x/12=20
X=48
As you see this is far too complicated

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 Post subject: Re: Help pleasePosted: Fri Jan 02, 2015 1:42 pm

Joined: Wed Sep 17, 2014 7:07 pm
Posts: 109
so the group is 30 children.
If that were so, how could you have 3/4 as a whole number?

More generally, it's unhelpful that the question as posed by the OP does not appear to specify whether or not any of the group likes neither football nor swimming. In the absence of that, is it not correct that an answer of 36 (T) can be proposed viz:

Football (F) 24 (of whom (FS) 20 like swimming)
Swimming (S) 27 (of whom (FS) 20 like football)
Neither football nor swimming (N) 5

and in which case would it not be

FS 20
F not S 4
S not F 7
N 5
T = 36

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 Post subject: Re: Help pleasePosted: Fri Jan 02, 2015 1:57 pm

Joined: Fri Nov 11, 2011 10:00 pm
Posts: 5418
Location: RBK
question is not well designed. Class size could even be 60.

Edited
Correct answer is 36 as above

Last edited by tiffinboys on Sun Jan 04, 2015 10:39 am, edited 1 time in total.

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 Post subject: Re: Help pleasePosted: Fri Jan 02, 2015 11:03 pm

Joined: Sat Aug 10, 2013 11:46 am
Posts: 188
It can't be 60:

Number only liking football = 25

Number only liking swimming = 20

Number only liking both = 20

Number liking neither = 5

Total = 70

I think 36 is the only other possible.

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