Final answer:
To find the total number of people surveyed in a scenario where specific percentages like different drinks and a certain number do not like either, we use the inclusion-exclusion principle, draw a Venn diagram, and solve for 'n' using the given percentages. The total number of people surveyed in this case is found to be 450.
Step-by-step explanation:
To find the total number of people in a survey where 80% like Coke, 85% like Pepsi, and 75% like both, but 45 people do not like either, we can use the principle of inclusion-exclusion. We start by drawing a Venn diagram to visualize the problem.
Let's denote the total number of people surveyed as 'n'. According to the inclusion-exclusion principle:
The number of people who like Coke (C) is 0.80n.
The number of people who like Pepsi (P) is 0.85n.
The number of people who like both (B) is 0.75n.
So the total number of people who like at least one of the drinks can be calculated as follows:
The number of people who like Coke or Pepsi or both = People who like Coke + People who like Pepsi - People who like both
In terms of the survey,
0.80n + 0.85n - 0.75n = n - 45
This simplifies to:
0.90n = n - 45
Rearranging, we get:
n - 0.90n = 45
0.10n = 45
n = 45 / 0.10
n = 450
Therefore, the total number of people surveyed is 450.