A group of 75 students was surveyed about their preferred summer vacation activities. Out of these 75 students, 27 preferred swimming, 35 preferred boxing, and 28 preferred football. 10 of these students preferred exactly 2 out of the three activities. 5 students did not prefer any of these three activities meaning they could prefer to choose any, or all, or none at any point in time. What was the maximum number of students that preferred exactly one of these three activities?
Question
A group of 75 students was surveyed about their preferred summer vacation activities. Out of these 75 students, 27 preferred swimming, 35 preferred boxing, and 28 preferred football. 10 of these students preferred exactly 2 out of the three activities. 5 students did not prefer any of these three activities meaning they could prefer to choose any, or all, or none at any point in time. What was the maximum number of students that preferred exactly one of these three activities?
Solution
To find the maximum number of students that preferred exactly one of these three activities, we need to consider the different possibilities.
Let's start by subtracting the students who preferred exactly 2 out of the three activities from the total number of students. We know that 10 students preferred exactly 2 activities, so we subtract 10 from the total of 75:
75 - 10 = 65
Now, let's subtract the students who did not prefer any of the three activities from this result. We know that 5 students did not prefer any of the activities, so we subtract 5 from the previous result:
65 - 5 = 60
Therefore, the maximum number of students that preferred exactly one of these three activities is 60.
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