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A survey of 1,200 tourists visiting Orlando was taken. Of those surveyed:

281 tourists had visited the Magic Kingdom
280 tourists had visited LEGOLAND
98 tourists had visited both the Magic Kingdom and LEGOLAN
100 tourists had visited both the Magic Kingdom and Universal Studios
98 tourists had visited both LEGOLAND and Universal Studios
34 tourists had visited all three theme parks
70 tourists did not visit any of these theme parks
How many tourists only visited Universal Studios?
a) 49
b) 64
c) 30
d) 61

1 Answer

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Final answer:

To determine how many tourists only visited Universal Studios, a calculation using the principle of inclusion and exclusion was performed, revealing that 61 tourists visited only Universal Studios.

Step-by-step explanation:

To calculate how many tourists only visited Universal Studios, we must first consider the principle of inclusion and exclusion. Let's begin by summing the number of tourists that visited each park:

  • 281 tourists had visited the Magic Kingdom.
  • 280 tourists had visited LEGOLAND.
  • Those who visited both the Magic Kingdom and LEGOLAND are 98.
  • Those who visited both the Magic Kingdom and Universal Studios are 100.
  • Those who visited both LEGOLAND and Universal Studios are 98.
  • Those who visited all three theme parks are 34.

The total number of tourists surveyed is 1,200, and 70 did not visit any of the parks. We can calculate the number of tourists who only visited Universal Studios by using the formula:

Total = Magic Kingdom only + LEGOLAND only + Universal Studios only + Magic Kingdom and LEGOLAND - Both + Magic Kingdom and Universal Studios - Both + LEGOLAND and Universal Studios - Both + All three - Each intersection twice + None

Therefore, to find the number of tourists who only visited Universal Studios, we need to subtract the intersections from the total:

Universal Studios only = Total - Magic Kingdom - LEGOLAND - None + Magic Kingdom and LEGOLAND + Magic Kingdom and Universal Studios + LEGOLAND and Universal Studios - All three

Plugging in the values we have:

Universal Studios only = 1200 - 281 - 280 - 70 + 98 + 100 + 98 - 34

Universal Studios only = 1200 - 561 + 296 - 34

Universal Studios only = 831 + 296 - 34

Universal Studios only = 1127 - 34

Universal Studios only = 1093 - 34

Universal Studios only = 61

So the correct answer is d) 61 tourists.

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