How do I solve this problem?

Question

A survey of 900 households revealed that 400 had only a TV, 200 had only a computer, and 100 had neither a TV nor a computer. How many households have both a TV and a computer?

Answer 1

You may use Boolean algebra (logical expressions), but a Venn Diagram is pretty easy:

 

Imagine (sorry, I can't draw it) two intersecting circles in a rectangle:

 

 

   900 total

*********************************************************************

*      A

*                           TV                                     Computer

*                           B                                       C

*                                             D

*

*Circle 1 is TV and includes  B and D.

*Circle 2 is Computer and includes C and D.

Note that D is included in both Circle 1 and Circle 2.  "How many households have both a TV and a computer?" means to find D.   A is included in the "Universe," but is outside of the circles [that is, "neither."]

 

"400 had only a TV"  means B=400

"200 had only a computer"   means C=200

"100 had neither a TV nor a computer"   means A=100

"survey of 900 households"   means   A + B + C + D = 900

 

           100 + 400 + 200 + D = 900

               700 + D = 900

                    D = 200

There were 200 households with both a TV and a computer.