SOLUTION: A survey of 100 photographers found: 60 take black and white photographs, 75 take color photographs and 45 take both types of photographs. a. How many take color, but not black

The red circle contains the 60 photographers that take black and white
photographs.  They are split between the regions a and b, and we don't yet
know how many of the 60 go in region a and how many go in region b.

The blue circle contains the 75 photographers that take color photographers.
They are split between the regions b and c, and we don't yet know how many
of the 75 go in region b and how many go in region c.

The three regions a,b and c contain:
1. The photographers in region a take ONLY black and white photographs. 
2. The photographers in region b take BOTH black and white photographs and
   color photographs.
3. The photographers in region c take ONLY color photographs.

Now we have something definite. We know that region b contains 45
photographers.  So we write 45 in region b, the middle region, the
overlapping part of the two circles:



Now since we know that the red circle contains 60 photographers and that
the overlapping part contains 45, we know that region a contains the other
60-45 or 15 photographers.  So we put 15 in the leftmost region, region a:



Now we see that the red circle contains a total of 60 photographers. Since
we know that the blue circle contains 75 photographers and that the
overlapping part b contains 45, we know that region a contains the other 
75-45 or 30 photographers.  So we put 30 in the rightmost region, region c:



Now you see that the blue circle contains a total of 75 photographers.  The
question is:

Answer: 30

Edwin