a survey of 1,168 tourists visiting orlando was taken. of those surveyed:
266 tourists had visited legoland
295 tourists had visited universal studios
87 tourists had visited both the magic kingdom and legoland
68 tourists had visited both the magic kingdom and universal studios
91 tourists had visited both legoland and universal studios
16 tourists had visited all three theme parks
74 tourists did not visit any of these theme parks
how many tourists only visited the magic kingdom (of these three)?

624 tourists only visited the Magic Kindgom.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of this set.

I am going to say that:

-The set A represents the tourists that visited LEGOLAND

-The set B represents the tourists that visited Universal Studios

-The set C represents the tourists that visited Magic Kingdown.

-The value d is the number of tourists that did not visit any of these parks, so:

We have that:

In which a is the number of tourists that only visited LEGOLAND, is the number of tourists that visited both LEGOLAND and Universal Studies, is the number of tourists that visited both LEGOLAND and the Magic Kingdom. and is the number of students that visited all these parks.

By the same logic, we have:

This diagram has the following subsets:

There were 1,168 tourists suveyed. This means that:

We start finding the values from the intersection of three sets.

The problem states that:

16 tourists had visited all three theme parks. So:

91 tourists had visited both LEGOLAND and Universal Studios. So:

68 tourists had visited both the Magic Kingdom and Universal Studios. So

87 tourists had visited both the Magic Kingdom and LEGOLAND

295 tourists had visited Universal Studios

266 tourists had visited LEGOLAND

How many tourists only visited the Magic Kingdom (of these three)?

This is the value of c, the we can find in the following equation:

624 tourists only visited the Magic Kindgom.