Final answer:
By using a Venn Diagram and the principle of inclusion-exclusion, we find that 200 households surveyed have both a TV and a computer.
Step-by-step explanation:
To solve the problem using a Venn Diagram, we begin by drawing two intersecting circles, one for TV owners and one for computer owners. Next, we input the given information. We know there are 700 households in total. According to the survey, 300 households have only a TV and 100 have only a computer, while 100 have neither TV nor computer. To find how many households have both a TV and a computer, we use the principle of inclusion-exclusion.
First, we subtract the number of households with neither a TV nor a computer from the total number of households:
Total with either TV, computer, or both = 700 (total households) - 100 (neither) = 600
Next, we subtract the households that have only one of the two devices:
Total with both TV and computer = 600 (total with either or both) - 300 (only TV) - 100 (only computer)
Now we simply subtract:
600 - 300 - 100 = 200
Therefore, 200 households have both a TV and a computer.