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:
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.]
We do as suggested, we start at the bottom of the list of clues and go
backwards.
3 bought all three
So we put h=3
7 bought records and T-shirts
So g+h=7, h=3, so g=4
10 bought books and T-shirts
So h+i=10, h=3, so i=7
8 bought books and records
So e+h=8, h=3, so e=5
10 bought books and T-shirts
So h+i=10, h=3, so i=7
26 bought T-shirts
So g+h+i+j=26, g=4,h=3,i=7, so j=12
22 bought books
So e+f+h+i=22,e=5,h=3,i=7, so f=7
20 bought records
So d+e+g+h=20,e=5,g=4,h=3, so d=8
A cashier observed the purchases of 38 people
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
a) How many bought T-shirts and records but not books?
That's g=4
b) How many bought only books?
That's f=7
c) How many people did not buy anything?
That's k=3
Now do it with the numbers in your problem, step-by-step.
Edwin
