Venn Diagram word problem: cricket (C) and football (F)

[SuchBants]

Question:
A group of 40 people were asked whether they like cricket (C) and football (F).
The number liking both cricket and football was 3 times the number liking only cricket.
Adding 3 to the number liking only cricket and doubling the answer equals the number of people liking only football.
Four said they did not like sport at all.
(a) complete the venn diagram.
(b) calculate n(C (intersect) F)
(c) calculate n(C (intersect) F')
(d) calculate n(C' (intersect) F)


My attempt:

C (intersect) F = 3c
F = 2(c+3) = 2c + 6

Im not sure if:

c = (40-4) -3c-(2c+6)
= 42 -c
c = 21

 

[Ishuda]

Question:
A group of 40 people were asked whether they like cricket (C) and football (F).
The number liking both cricket and football was 3 times the number liking only cricket.
Adding 3 to the number liking only cricket and doubling the answer equals the number of people liking only football.
Four said they did not like sport at all.
(a) complete the venn diagram.
(b) calculate n(C (intersect) F)
(c) calculate n(C (intersect) F')
(d) calculate n(C' (intersect) F)


My attempt:

C (intersect) F = 3c
F = 2(c+3) = 2c + 6

Im not sure if:

c = (40-4) -3c-(2c+6)
= 42 -c
c = 21

It looks like you may be mixing those who like cricked with those who only liked cricket. To distinguish let
Co = like cricket only
Cf = like cricket and football
C = those who like cricket = Co + Cf
Fo = like football only
Fc = like football and cricket
F = those who like football = Fo + Fc
N = do not like sport at all = 4

Now start with what we are given
C + F + N = 40
3 Co = Cf + Fc
and continue from there