SOLUTION: As part of his project,a final year student of music, interviewed some undergraduate students, on the type of music they liked listening to;30 liked listening to jazz,20 liked list

Algebra ->  sets and operations -> SOLUTION: As part of his project,a final year student of music, interviewed some undergraduate students, on the type of music they liked listening to;30 liked listening to jazz,20 liked list      Log On


   

Question 1145819: As part of his project,a final year student of music, interviewed some undergraduate students, on the type of music they liked listening to;30 liked listening to jazz,20 liked listening to Reggae while 20 also liked to funk.10 students liked listening to jazz and Reggae,10 students liked jazz and funk while 9 students liked to Raggae and funk.if 3students liked listening to all the three music,32 did not like listening to any of the three types of music;find;1. The number that liked listening to jazz only.2: the number that liked listening to funk only;3.the number that liked listening to Raggae only.4.the total number of undergraduate students that were interviewed.
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!

Jazz = 30
Reggae = 20
Funk = 20

Jazz & Reggae = 10
Jazz & Funk = 10
Reggae & Funk = 9

Jazz, Reggae, & Funk = 3

None of the three = 32

=====================================

Jazz, Reggae, & Funk = 3

Jazz & Reggae (ONLY) = 10 (Jazz & Reggae) - 3 (Jazz, Reggae, & Funk) = 7
Jazz & Funk (ONLY) = 10 (Jazz & Funk) - 3 (Jazz, Reggae, & Funk) = 7
Reggae & Funk (ONLY) = 9 (Reggae & Funk) - 3 (Jazz, Reggae, & Funk) = 6

Jazz (ONLY) or Jazz & Reggae (ONLY) or Jazz & Funk (ONLY) = 30 (Jazz) - 3 (Jazz, Reggae, & Funk) = 27
Reggae (ONLY) or Jazz & Reggae (ONLY) or Reggae & Funk (ONLY) = 20 (Reggae) - 3 (Jazz, Reggae, & Funk) = 17
Funk (ONLY) or Jazz & Funk (ONLY) or Reggae & Funk (ONLY) = 20 (Funk) - 3 (Jazz, Reggae, & Funk) = 17

=====================================

Jazz & Reggae (ONLY) = 7
Jazz & Funk (ONLY) = 7
Reggae & Funk (ONLY) = 6

Jazz (ONLY) = 27 (Jazz (ONLY) or Jazz & Reggae (ONLY) or Jazz & Funk (ONLY)) - 7 (Jazz & Reggae ONLY) - 7 (Jazz & Funk ONLY) = 13
Reggae (ONLY) = 17 (Reggae (ONLY) or Jazz & Reggae (ONLY) or Reggae & Funk (ONLY)) - 7 (Jazz & Reggae ONLY) - 6 (Reggae & Funk ONLY) = 4
Funk (ONLY) = 17 (Funk (ONLY) or Jazz & Funk (ONLY) or Reggae & Funk (ONLY)) - 7 (Jazz & Funk ONLY) - 6 (Reggae & Funk ONLY) = 4

=====================================

In summary:

Jazz (ONLY) = 13
Reggae (ONLY) = 4
Funk (ONLY) = 4

Jazz & Reggae (ONLY) = 7
Jazz & Funk (ONLY) = 7
Reggae & Funk (ONLY) = 6

Jazz, Reggae, & Funk = 3

None of the three = 32

=====================================

1. The number that liked listening to only jazz = 13
2. The number that liked listening to only funk = 4
3. The number that liked listening to only reggae = 4
4. The total number of undergraduate students that were interviewed = 76