A survey of 30 people finds that 16 are teachers, 12 own motorcycles, and 8 are neither. How many own motorcycles?
14 people own motorcycles.
In a survey of 30 people, where 8 are neither teachers nor motorcycle owners, we can calculate the number of motorcycle owners by subtracting the non-participants from the total. This calculation reveals that 22 people are either teachers or motorcycle owners, and among them, 12 people own motorcycles.
This choice represents the number of motorcycle owners given in the problem statement. However, it does not account for the 8 individuals who do not fit into either category. Thus, the calculation requires further analysis of the remaining participants.
This is the correct answer. By subtracting the 8 people who are neither teachers nor motorcycle owners from the total of 30, we find that 22 people are either teachers or motorcycle owners. Since 16 are teachers, this implies that 22 - 16 = 6 individuals must be both teachers and motorcycle owners. Therefore, the total number of motorcycle owners is 12 (from the problem statement) plus the 6 who are counted among the teachers, yielding 14 motorcycle owners.
This value corresponds to the number of teachers in the survey. While it is true that some teachers may own motorcycles, this number does not reflect the total count of motorcycle owners. The calculation must consider the overlap between teachers and motorcycle owners to find the accurate total.
This number is incorrect as it exceeds the total number of participants who are either teachers or motorcycle owners. Given the constraints of the problem, there cannot be 18 motorcycle owners when only 30 individuals are surveyed and some of them are neither.
The problem requires a careful interpretation of the relationships between motorcycle owners and teachers among the surveyed individuals. After discerning the total number of participants, subtracting those who are neither reveals that 14 people own motorcycles, factoring in the overlaps between the groups. This process highlights the importance of understanding set intersections in survey data.
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