# Math Word Problem?

A survey of 77 college students was taken to determine the musical styles they liked. Of those, 31 students listened to rock, 26 to classical, and 29 to jazz. Also, 15 students listened to rock and jazz, 14 to rock and classical, and 10 to classical and jazz. Finally, 7 students listened to all three musical styles. Construct a Venn diagram and determine the cardinality for each region. Use the completed Venn Diagram to answer the following questions.

How many listened to only rock music?

### 2 Answers

- King LeoLv 71 month ago
cardinality = n

n( Rock ) = 31

n( Classical ) = 26

n( Jazz ) = 29

n( Rock & Jazz ) = 15

n( Rock & Classical ) = 14

n( Classical & Jazz ) = 10

n( all three ) = 7

- PuzzlingLv 71 month ago
Start in the middle with the 7 that liked all three.

Subtract that from each of the sets of students that liked at least two genres and put that in the overlap for each pair. (For example 8 students liked *only* rock and jazz).Finally figure out what is left for the regions of rock only, classical only and jazz only.

At the end, add up all seven regions and subtract from 77, for the students that didn't like any musical style.