Sets and Applications of Venn Diagrams

[KathleenLaura]

Could someone please help me figure out this word problem using a Venn Diagram? After a certain point I am just stuck! It would really help if I could see the steps in order to solve it too! Thanks!

In a recent survey, people were asked which radio station they listened to on a regular basis. The following results were obtained: 140 listened to WOLD (oldies), 95 listened to WJZZ (jazz), 134 listened to WTLK (talk show news), 235 listened WOLD or WJZZ, 48 listened to WOLD and WTLK, 208 listened to WTLK or WJZZ, and 25 listened to none.

a. What percent of people in the survey listened only to WTLK on a regular basis?

b. What percent of people in the survey did not listen to WTLK on a regular basis?

[nona.m.nona]

Could someone please help me figure out this word problem using a Venn Diagram? After a certain point I am just stuck!

Please show your work up to this "certain point". Thank you.

In a recent survey, people were asked which radio station they listened to on a regular basis. The following results were obtained: 140 listened to WOLD (oldies), 95 listened to WJZZ (jazz), 134 listened to WTLK (talk show news), 235 listened WOLD or WJZZ, 48 listened to WOLD and WTLK, 208 listened to WTLK or WJZZ, and 25 listened to none.

a. What percent of people in the survey listened only to WTLK on a regular basis?

b. What percent of people in the survey did not listen to WTLK on a regular basis?

To learn how Venn diagrams may be applied to exercises of this type, please study this topical lesson.

Since there are three radio stations involved in this particular exercise, it would be useful to start by drawing the standard three overlapping circles, labelling each with the call-letters of the respective station. Note that, due to the inclusion of a "none" condition, it may be useful also to draw a "universe" box surrounding the three circles, so that the "25" label is understandable and does not get misplaced.