Final answer:
65 people must have dual passports. However, this answer does not match the given options, suggesting there may be an error in the question or the options.
Step-by-step explanation:
To determine how many people have dual passports (US and Canadian), we can use the principle of inclusion-exclusion. The principle says that for any two sets, the size of their union is the sum of the sizes of the individual sets minus the size of their intersection (the part that is common to both).
Firstly, let's define our sets:
The union of the Canadian and US passport holders should equal the total number of people minus those with no passports (145 - 30), which is 115. This is the sum of Canadian passport holders and US passport holders minus the number of dual passport holders, which we're trying to find.
Using the formula:
Union of two sets = Size of Set A + Size of Set B - Both A and B (intersection)
115 = 95 + 85 - (Both Canadian and US passports)
Now, let's find out the number of people with both passports:
115 = 180 - (Both Canadian and US passports)
(Both Canadian and US passports) = 180 - 115
(Both Canadian and US passports) = 65
However, since our options don't include 65, we realize there's an error in calculation due to the fact that the union of Canadian and US passport holders (115) cannot be more than the total number of people in the reunion (145). So, we need to adjust our approach.
The correct approach is:
(Both Canadian and US passports) = (Number of Canadian passport holders) + (Number of US passport holders) - (Total number of people at the reunion with at least one passport)
(Both Canadian and US passports) = 95 + 85 - (145 - 30)
(Both Canadian and US passports) = 180 - (115)
(Both Canadian and US passports) = 65
Given the principle of inclusion-exclusion, the number of people with dual passports is therefore 65.
However, since the number 65 is not an option, we need to reassess our computations, as the principle of inclusion-exclusion must yield a number that is part of the options provided.
Upon re-evaluating our method, we notice that we should subtract the number of people without any passports from the total number of people in the reunion before calculating the number of dual passports. This gives us:
(Both Canadian and US passports) = 95 + 85 - (145 - 30)
(Both Canadian and US passports) = 180 - 115
(Both Canadian and US passports) = 65
Therefore, the correct number of people with dual passports is 65, so there is likely an error in the provided options or the question itself.