Question 1167791
<pre>
Instead of doing your problem for you, I'll do another EXACTLY like it,
step-by-step, which you can use as a guide for doing yours.  The one I'll
do has these numbers instead of yours:
</pre>
The Spirit Shop had a sale on records, books, and T-shirts. A cashier observed
the purchases of 38 people and found that:
20 bought records
22 bought books
26 bought T-shirts
8 bought books and records
10 bought books and T-shirts
7 bought records and T-shirts
3 bought all three
Draw a Venn diagram with the number of people in each area to represent this
information and answer the questions. [Hint: Start at the bottom of the list.]

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"d=?"),
locate(-3.5,-2,"k=?"),
locate(0,-2.7,T),
locate(-.45,-1,"j=?"),
locate(.6,.4,"i=?"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,R),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.5,.5,"g=?"),
locate(-.4,2.3,"e=?"),
locate(1.8,2,"f=?"),
locate(-.4,1.1,"h=?") )}}}<pre>

We do as suggested, we start at the bottom of the list of clues and go
backwards.

</pre>3 bought all three<pre>
So we put h=3

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"d=?"),
locate(-3.5,-2,"k=?"),
locate(0,-2.7,T),
locate(-.45,-1,"j=?"),
locate(.6,.4,"i=?"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,R),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.5,.5,"g=?"),
locate(-.4,2.3,"e=?"),
locate(1.8,2,"f=?"),
locate(-.4,1.1,"h=3") )}}}

</pre>7 bought records and T-shirts<pre>
So g+h=7, h=3, so g=4

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"d=?"),
locate(-3.5,-2,"k=?"),
locate(0,-2.7,T),
locate(-.45,-1,"j=?"),
locate(.6,.4,"i=?"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,R),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.5,.5,"g=4"),
locate(-.4,2.3,"e=?"),
locate(1.8,2,"f=?"),
locate(-.4,1.1,"h=3") )}}}

</pre>10 bought books and T-shirts<pre>
So h+i=10, h=3, so i=7
{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"d=?"),
locate(-3.5,-2,"k=?"),
locate(0,-2.7,T),
locate(-.45,-1,"j=?"),
locate(.6,.4,"i=?"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,R),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.5,.5,"g=4"),
locate(-.4,2.3,"e=?"),
locate(1.8,2,"f=?"),
locate(-.4,1.1,"h=3") )}}}

</pre>8 bought books and records<pre>
So e+h=8, h=3, so e=5

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"d=?"),
locate(-3.5,-2,"k=?"),
locate(0,-2.7,T),
locate(-.45,-1,"j=?"),
locate(.6,.4,"i=?"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,R),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.5,.5,"g=4"),
locate(-.4,2.3,"e=5"),
locate(1.8,2,"f=?"),
locate(-.4,1.1,"h=3") )}}}

</pre>10 bought books and T-shirts<pre>
So h+i=10, h=3, so i=7

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"d=?"),
locate(-3.5,-2,"k=?"),
locate(0,-2.7,T),
locate(-.45,-1,"j=?"),
locate(.6,.4,"i=7"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,R),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.5,.5,"g=4"),
locate(-.4,2.3,"e=5"),
locate(1.8,2,"f=?"),
locate(-.4,1.1,"h=3") )}}}

</pre>26 bought T-shirts<pre>
So g+h+i+j=26, g=4,h=3,i=7, so j=12

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"d=?"),
locate(-3.5,-2,"k=?"),
locate(0,-2.7,T),
locate(-.45,-1,"j=12"),
locate(.6,.4,"i=7"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,R),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.5,.5,"g=4"),
locate(-.4,2.3,"e=5"),
locate(1.8,2,"f=?"),
locate(-.4,1.1,"h=3") )}}}

</pre>22 bought books<pre>
So e+f+h+i=22,e=5,h=3,i=7, so f=7  


{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"d=?"),
locate(-3.5,-2,"k=?"),
locate(0,-2.7,T),
locate(-.45,-1,"j=12"),
locate(.6,.4,"i=7"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,R),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.5,.5,"g=4"),
locate(-.4,2.3,"e=5"),
locate(1.8,2,"f=7"),
locate(-.4,1.1,"h=3") )}}}

</pre>20 bought records<pre>
So d+e+g+h=20,e=5,g=4,h=3, so d=8

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"d=8"),
locate(-3.5,-2,"k=?"),
locate(0,-2.7,T),
locate(-.45,-1,"j=12"),
locate(.6,.4,"i=7"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,R),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.5,.5,"g=4"),
locate(-.4,2.3,"e=5"),
locate(1.8,2,"f=7"),
locate(-.4,1.1,"h=3") )}}}

</pre>A cashier observed the purchases of 38 people<pre>
So d+e+f+g+h+i+j+k=38,d=8,e=5,f=7,g=4,h=3,i=7,j=12, so k=3</pre>

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"d=8"),
locate(-3.5,-2,"k=3"),
locate(0,-2.7,T),
locate(-.45,-1,"j=12"),
locate(.6,.4,"i=7"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,R),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.5,.5,"g=4"),
locate(-.4,2.3,"e=5"),
locate(1.8,2,"f=7"),
locate(-.4,1.1,"h=3") )}}}

</pre>a) How many bought T-shirts and records but not books?<pre>
That's g=4
</pre>b) How many bought only books?<pre>
That's f=7
</pre>c) How many people did not buy anything?<pre>
That's k=3

Now do it with the numbers in your problem, step-by-step.

Edwin</pre>