SOLUTION: In a certain club, 14 members speak Spanish, 7 members speak Creole and 4 members speak both Creole or Spanish, and 37 members speak neither Creole nor Spanish. Find the numbers o

You can do this either by a Venn diagram or by a formula.

I'll first do it by a Venn diagram and then I'll do it
using a formula.

VENN DIAGRAM METHOD:

Imagine you have all the members in the bleachers of football field.
 
First draw a big rectangle to represent, say, a big football field,
for all the club members to come down and stand in.
 

 
Now on that football field draw a big circle for all 14 members
to stand in who speak Spanish and label it S:


 
Next draw another big circle overlapping it for all 7 members
to stand in who speak Creole and label it C:
 

 
Now the 37 members who speak neither Creole nor Spanish will have 
to stand on the field outside both circles, so we'll write 37 out 
there to stand for the 37 students who will stand out there:
 

 
The 4 members who speak both Creole and Spanish will be standing 
in both circles, that is, they will be standing in the overlapping 
part of the two circles, so we'll write 4 in the overlapping part
to stand for the 4 members who will stand there.
 
`                   
 
and in the main drawing:
 

 
Since there are 14 members who speak Spanish, the rest of those 14
besides the 4 that speak both languages, that is, 14-4, or 10, will 
have to stand in this region, in which we write 10:
 
  
 
and in the main drawing:
 

 
Since there are 7 members who speak Creole, the rest of those 7
besides the 4 that speak both languages, that is, 7-4, or 3, will
have to stand in this region, in which we write 3:

 
`                      `  
 
and in the main drawing:
 

 
Now we add up all the numbers in the four regions and
that sum must be all the club members standing somewhere
on the football field:
 
37+10+4+3 = 54

The answer is: There are 54 members in the club.

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FORMULA METHOD:

N(S or C) = N(S) + N(C) - N(S and C)

N(S or C) = 14 + 7 - 4

N(S or C) = 17

Now the total number of members in the club =

N(S or C) + N[not(S or C)]

17 + 37 = 54 members in the club

Edwin