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Directions: Answer the questions based on the information given below.
A survey is conducted among people about the type of 'music' genres (Folk, Rock, and Jazz) they prefer to listen. Each of the person prefer to listen at least one or more genres.The number of people who prefer to listen only 'Folk', only 'Rock and only 'Jazz' are in the ratio of 56 : 79 : 41. The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' is 25% less the number of people who prefer to listen all three 'music' genres. The number of people who prefer to listen both 'Rock' and 'Jazz' but not 'Folk' and both 'Folk' and 'Rock' but not 'Jazz' are 50 and 35 respectively. The number of people who prefer to listen only 'Jazz' are five less than six times of the people who prefer to listen both 'Folk' and 'Rock' but not 'Jazz'. The total number of people who prefer to listen exactly two type of 'music' genres is equal to 130.
What is the ratio between the number of people who prefer to listen 'Folk' and to 'Jazz'?
3 : 2
5 : 4
7 : 6
9 : 8
11 : 10
- Let the number of people who prefer only 'Folk', only 'Rock', and only 'Jazz' be 56x, 79x, and 41x, respectively.
- The number of people who prefer both 'Folk' and 'Jazz' but not 'Rock' is 25% less than those who prefer all three genres. Let the all-three-genres number be _a_; then 'Folk' and 'Jazz' is 0.75a.
- Given:
- 'Rock' and 'Jazz' (not 'Folk') = 50
- 'Folk' and 'Rock' (not 'Jazz') = 35
- The statement "the number of people who prefer only 'Jazz' are five less than six times of the people who prefer both 'Folk' and 'Rock' but not 'Jazz'" translates to:
- 41x = 6 * 35 - 5
- Solve for x to get the total counts for only 'Folk', 'Rock', and 'Jazz'.
- Total people preferring exactly two genres = 130 = 0.75a + 50 + 35
- Solve for _a_.
- Now, calculate 'Folk' + 'Jazz' = only 'Folk' + only 'Jazz' + 0.75a.
- Calculate the ratio between people who prefer 'Folk' and 'Jazz'.
- The correct answer is 3: 2
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