Hello, sfspitfire23!

This is a tricky one . . .

$\displaystyle \text{A group of youths was studied. 68\% have a television,}$

. . $\displaystyle \text{92\% have a CD/tape player, and 32\% have a personal computer.}$

$\displaystyle \text{Only 4\% have none of the above.}$

$\displaystyle \text{9\% have a PCr and a CD player but no TV.}$

$\displaystyle \text{44\% have a TV and a CD/ player but no PC.}$

$\displaystyle \text{1\% have a TV and PC but no CD player.}$

$\displaystyle \text{How would I fill out the Venn diagram?}$

Construct the Venn diagram and fill in the known quantities.

Code:

o---------------------------------------------------o
| |
| o-----------------------o |
| | TV | |
| | b o-------+---------------o |
| | | | CD | |
| | | 44 | c | |
| | | | | |
| | o-------+-------+-------o | |
| | | | | | | |
| | | 1 | a | | | |
| | | | | | | |
| o-------+-------+-------o | | |
| | | 9 | | |
| | | | | |
| | o---------------+-------o . . |
| | d | |
| | PC | |
| 4 o-----------------------o |
| |
o---------------------------------------------------o

Use $\displaystyle a,b,c,d$ in the unknown spaces.

In the TV-circle, the total is 68.

. . $\displaystyle a + b +45 \:=\:68 \quad\Rightarrow\quad a + b \:=\:23 \;\;[1]$

In the CD-circle, the total is 92.

. . $\displaystyle a + c + 53 \:=\:92 \quad\Rightarrow\qud a + c \:=\:39 \;\;[2]$

In the PC-circle, the total is 32.

. . $\displaystyle a + d + 10 \:=\:32 \quad\Rightarrow\quad a + d \:=\:22\;\;[3]$

In the three circles, the total is 96.

. . $\displaystyle a + b + c + d + 54 \:=\:96 \quad\Rightarrow\quad a + b + c + d \:=\:42 \;\;[4]$

Subtract [2]-[1]: .$\displaystyle c - b \:=\:16\;\;[5]$

Subtract [2]-[3]: .$\displaystyle c - d \:=\:17\;\;[6]$

Subtract [4]-[1]: .$\displaystyle c + d \:=\:19\;\;[7]$

Add [6]+[7]: .$\displaystyle 2c \:=\:36 \quad\Rightarrow\quad \boxed{c \,=\,18}$

Substitute into [7]: .$\displaystyle 18 + d \:=\:19 \quad\Rightarrow\quad \boxed{d \,=\,1}$

Substitute into [5]: .$\displaystyle 18 - b \:=\:16 \quad\Rightarrow\quad \boxed{b \,=\,2}$

Substitute into [1]: .$\displaystyle a + 16 2 \:=\:23 \quad\Rightarrow\quadn \boxed{a \,=\,21}$

Now you can fill in the rest of the Venn diagram . . .