Final answer:
After setting up equations and solving for x, where x represents the number of families who drink both tea and coffee, the answer calculated is 60. However, this does not match any of the provided options, indicating a possible error in the question or answer choices.
Step-by-step explanation:
To solve the question of finding the number of families who drink both tea and coffee, we need to use the concepts of set theory and Venn diagrams. Given that 710 families drink tea and 230 drink coffee out of 1000 families, let's call the number of families that drink both tea and coffee 'x'. We also know that the families that drink both are half the number of families who drink neither. So we can set up equations based on the total number of families (1000).
- Total number of families = 1000
- Families drinking tea = 710
- Families drinking coffee = 230
- Families drinking both tea and coffee = x
- Families drinking neither = 1000 - (710 + 230 - x)
According to the problem, the number of families drinking both tea and coffee is half of those drinking neither, which gives us the equation:
x = (1000 - (710 + 230 - x)) / 2
Simplifying the equation, we get:
x = (1000 - 940 + x) / 2
x = (60 + x) / 2
Now, solving for x:
2x = 60 + x
x = 60
Therefore, the number of families that drink both tea and coffee is 60. However, this answer does not match any of the options provided, which suggests a possible mistake in the question or the available options. If it's a mistake in the original survey data or a typo in the question options, we would advise checking the data or clarifying the available answers.