Question 1141272
{{{drawing(300,200,-4,4,-2,4.8, locate(-2,1.8,a),locate(1.5,1.7,c), locate(-3.8,2.5,BW), locate(-.1,1.8,b),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,Col)
 )}}}
60 take black and white photographs,<pre>
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.
</pre>75 take color photographs<pre>
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.
</pre>and 45 take both types of photographs<pre>
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:

{{{drawing(300,200,-4,4,-2,4.8, locate(-2,1.8,a),locate(1.5,1.7,c), locate(-3.8,2.5,BW), locate(-.1,1.8,45),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,Col)
 )}}}

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:

{{{drawing(300,200,-4,4,-2,4.8, locate(-2,1.8,15),locate(1.5,1.7,c), locate(-3.8,2.5,BW), locate(-.1,1.8,45),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,Col)
 )}}}

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:

{{{drawing(300,200,-4,4,-2,4.8, locate(-2,1.8,15),locate(1.5,1.7,30), locate(-3.8,2.5,BW), locate(-.1,1.8,45),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,Col)
 )}}}

Now you see that the blue circle contains a total of 75 photographers.  The
question is:
</pre> How many take color, but not black and white photographs?<pre>
Answer: 30

Edwin</pre>