In a class of 100 students, 16 take Chorus, 30 take Band, and 10 take both Chorus and Band. How many students in the class are not enrolled in either Chorus or Band?
10 take both ... that is the intersection area of band and chorus
16 take chorus ... but 10 of those take both ... so 6 are only chorus
30 take chorus ... but 10 of those take both ... so 20 are only band
10 + 6 + 20 = 36 ... students in band or chorus or both
100 - 36 = 64 ... students not in either Chorus or Band
make a Venn diagram ... the intersecting circles
I did!
Now what do i do?
Thanks R_scott.
To find the number of students who are not enrolled in either Chorus or Band, we need to subtract the number of students who are enrolled in either Chorus or Band from the total number of students in the class.
First, let's find the number of students who are enrolled in either Chorus or Band. This can be done using the principle of inclusion-exclusion.
The total number of students enrolled in Chorus is given as 16 and the total number of students enrolled in Band is given as 30. However, 10 students are enrolled in both Chorus and Band.
So, to find the number of students who are enrolled in either Chorus or Band, we can add the number of students in each class (16 + 30) and then subtract the number of students enrolled in both classes (10).
16 + 30 - 10 = 36
Therefore, there are 36 students who are enrolled in either Chorus or Band.
To find the number of students who are not enrolled in either Chorus or Band, we subtract the number of students enrolled in either Chorus or Band (36) from the total number of students in the class (100).
100 - 36 = 64
Therefore, there are 64 students in the class who are not enrolled in either Chorus or Band.