SOLUTION: In a school of t students, x are enrolled in algebra, y in music, and b students are in both algebra and music. How many students are NOT in either algebra or music? A) t � (x +

Question 252790: In a school of t students, x are enrolled in algebra, y in music, and b students are in both algebra and music. How many students are NOT in either algebra or music?
A) t � (x + y) B) x + y � b C) t � (x + y - b) D) t � (x - y - b) E) t � b

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
answer should be selection C, which is:

t - (x + y - b)

here's why:

x is the number of students enrolled in algebra.
y is the number of students enrolled in music.
b is the number of students enrolled in algebra and music.

b is therefore included in both x and y, because if a student is enrolled in both, then the student is being counted in each. this means the student is being double counted.

the number of students enrolled in algebra and music is (x + y - b).

to find the number of students NOT enrolled in algebra and music, you have to subtract this from the total number of students to get:

t - (x + y - b)

example:

assume 15 students enrolled in algebra.
assume 15 dtudents enrolled in music.
assume 5 students enrolled in each.

total number of students enrolled in algebra and music is 25 (not 30).

this is because 5 students are enrolled in both and are being counted twice (once in algebra and once in music).

the 5 students are being counted as 10 students (5 in algebra and 5 in music).

in order to avoid double counting them, you need to subtract 5 from the total to get 25.

now you have:

10 students enrolled only in algebra.
10 students enrolled only in music.
5 students enrolled in both algebra and music.

total is 25 students.

assume the total number of students is 100, then the number of students NOT enrolled in algebra and music is 100 - 25 = 75.

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