# Venn Diagram with algebra

• Mar 17th 2010, 11:26 AM
Venn Diagram with algebra
A local radio station asked listeners which of the following types of music did they like: Pop, Rock or Rap.

Of the 44 listeners who responded, 18 said they like Rap.
9 said they like pop and rock only, 7 said they like pop and rap only.
While 1 person likes rock and rap only.
Three times as many said they like pop only as said they like all 3 types of music.
Twice as many said they like pop as said they like Rock.
3 people said they do not like any of this music.
Let x represent those listeners who like all 3 types of music.

i) Represent this on a venn diagram
ii) Calculate x
iii) Calculate the percentage of listeners who like one type of music only. Give your answer, correct to 1 decimal place.
• Mar 17th 2010, 11:59 AM
Quote:

A local radio station asked listeners which of the following types of music did they like: Pop, Rock or Rap.

Of the 44 listeners who responded, 18 said they like Rap.
9 said they like pop and rock only, 7 said they like pop and rap only.
While 1 person likes rock and rap only.
Three times as many said they like pop only as said they like all 3 types of music.
Twice as many said they like pop as said they like Rock.
3 people said they do not like any of this music.
Let x represent those listeners who like all 3 types of music.

i) Represent this on a venn diagram
ii) Calculate x
iii) Calculate the percentage of listeners who like one type of music only. Give your answer, correct to 1 decimal place.

Have you looked on this site for similar questions? Here is one I solved a little time ago. It doesn't have an $x$ in it, but the method is just the same. Read it through carefully - if you still can't see how to do your problem, get back to us and we'll take it from there.