Question 940201
<pre>
I think your teacher wants you to use a Venn diagram (also known as Euler
diagram) like this:

{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,a),locate(1.5,1.7,c),locate(-3.7,-1,d), locate(-3.6,2.5,R), 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,T)
 )}}}

The red circle represents a set R that contains all those who own a radio.

The blue circle represents a set T that contains all those who own a TV.

The left region of the red circle that has "a" in it are those who own
a Radio but do not own a TV.  

The middle region that has a "b" is part of both circles, and represents 
a set that contains all those who own BOTH a radio and a TV.
The right region of the blue circle that has "c" in it are those who own
a TV but do not own a radio.

The region that has "d" in it is outside of both circles.  It represents
the ones which have neither a radio nor a TV.  
</pre>
If 8 students don't own either of them,
<pre>
Therefore d=8, so we replace d by 8

{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,a),locate(1.5,1.7,c),locate(-3.7,-1,8), locate(-3.6,2.5,R), 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,T)
 )}}}
</pre> 
38 own a radio 
<pre>
Therefore a+b=38
</pre>
and 28 own a TV. 
<pre>
Therefore b+c=28
</pre>
out of 70 students,
<pre>
Therefore a+b+c+d=70, and since d=8,
a+b+c+8=70 or a+b+c=62

Subtracting these equations:

a+b+c=62
a+b  =38
--------
    c=24

Substituting in b+c=28
   b+24=28
      b=4

Substituting in 
    a+b=38
    a+4=38
      a=34

So the complete Venn diagram is

{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,34),locate(1.5,1.7,24),locate(-3.7,-1,8), locate(-3.6,2.5,R), locate(-.1,1.8,4),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,T)
 )}}} 
</pre>
what fraction of the students owns both a radio and TV
<pre>
That's the 4 in the middle region.

4 out of 70 is the fraction {{{4/70}}}.

Edwin</pre>