Of the students in a certain classroom, 9 are in the school play, 12 are in the orchestra, and 15 are in the choral group. If 5 students participate in exactly 2 of the 3 activities and all other students participate in only 1 activity. How many students are in the homerooooom?
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To find the number of students in the homeroom, we need to subtract the number of students participating in exactly 2 of the activities from the total number of students.
Let's denote the number of students in the classroom as "x".
Since 9 students are in the school play, 12 are in the orchestra, and 15 are in the choral group, we can add these numbers to find the total number of students participating in at least one activity:
9 + 12 + 15 = 36
However, we have counted the students participating in exactly 2 activities twice, so we need to subtract that:
36 - 2 * 5 = 36 - 10 = 26
Therefore, there are 26 students in the homeroom.
To find the number of students in the homeroom, we need to add up the number of students in each activity and then subtract the number of students who participate in exactly 2 of the activities twice (since they were counted in both activities).
Let's break it down step by step:
1. The number of students in the school play = 9.
2. The number of students in the orchestra = 12.
3. The number of students in the choral group = 15.
Now, let's calculate how many students participate in exactly 2 of the activities.
1. The number of students participating in the school play and orchestra = 5.
2. The number of students participating in the school play and choral group = 5.
3. The number of students participating in the orchestra and choral group = 5.
Next, we need to calculate how many students participate in all three activities. Since we already counted the students participating in exactly 2 of the activities, we subtract the total from each activity individually from the total number of students participating in exactly 2 of the activities.
1. The number of students participating in all three activities = 5 - (5 - 0) = 0.
2. The number of students participating in only the school play = 9 - (5 - 0) = 4.
3. The number of students participating in only the orchestra = 12 - (5 - 0) = 7.
4. The number of students participating in only the choral group = 15 - (5 - 0) = 10.
Finally, add up the number of students in each category:
Number of students participating in the school play = 9 (only the school play) + 5 (participating in 2 activities including the school play) = 14.
Number of students participating in the orchestra = 12 (only the orchestra) + 5 (participating in 2 activities including the orchestra) = 17.
Number of students participating in the choral group = 15 (only the choral group) + 5 (participating in 2 activities including the choral group) = 20.
To find the total number of students in the homeroom, we add the number of students in each category:
14 (students participating in the school play) + 17 (students participating in the orchestra) + 20 (students participating in the choral group) = 51.
Therefore, there are 51 students in the homeroom.