Solve the problem.
-A survey of a group of 112 tourists was taken in St. Louis. The survey showed the following: 63 of the tourists plan to visit Gateway Arch;
44 plan to visit the zoo;
9 plan to visit the Art Museum and the zoo, but not the gateway Arch;
14 plan to visit the Art Museum and the Gateway Arch, but not the zoo;
16 plan to visit the Gateway Arch and the zoo, but not the Art Museum;
7 plan to visit the Art Museum, the zoo, and the Gateway Arch;
14 plan to visit none of the three places.
How many plan to visit the Art Museum only?
A)14
B)32
C)98
D)44

Question

Quizplus · Accepted Answer

To find the number of tourists planning to visit only the Art Museum, we subtract those who plan to visit the Art Museum in combination with other attractions from the total number of tourists interested in the Art Museum. The total number of tourists interested in the Art Museum can be calculated by adding those who visit the Art Museum and the Gateway Arch (but not the zoo), those who visit the Art Museum and the zoo (but not the Gateway Arch), those who visit all three places, and those who visit the Art Museum only. However, the problem does not directly provide the total number of tourists interested in the Art Museum alone or in combination with other attractions. Instead, we are given specific combinations. To find the number of tourists visiting only the Art Museum, we need to consider the total survey count, subtract the number of tourists visiting none of the attractions, and then subtract the counts for each specific combination or single attraction visits, ensuring not to double-count those visiting multiple attractions. Given the information, we can't directly calculate the number of tourists visiting only the Art Museum without knowing the total number of tourists interested in the Art Museum. However, the correct approach involves subtracting the counts of tourists visiting the Art Museum in combination with other attractions from the total number interested in the Art Museum, which is not directly provided. The provided information allows us to calculate the number of tourists visiting only the Art Museum by subtracting those visiting it in combination with others from an unknown total, which requires additional information not given in the problem statement.

Solve the Problem. -A Survey of a Group of 112 Tourists Was Taken