Help please

[Success999]

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

[russet]

Draw an overlapping line diagram

[Ladymuck]

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?

[moved]

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.

[Ladymuck]

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.

[JRM]

The question tells you that 20 like both activities.

[Success999]

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

[equilibro]

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

[tiffinboys]

question is not well designed. Class size could even be 60.


Edited
Correct answer is 36 as above

[russet]

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.