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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.
Find the total number of people who prefer to listen only 'Folk' and only 'Rock'?
600
625
675
700
725
- Let's denote:
- People who prefer only Folk, only Rock, and only Jazz as F, R, and J respectively.
- According to the given ratio, F : R : J = 56 : 79 : 41.
- The people who prefer both Folk and Jazz, but not Rock, are 25% less than those who like all three genres.
- If x is the number of people who like all three genres, then 0.75x like both Folk and Jazz, but not Rock.
- People preferring both Rock and Jazz, but not Folk: 50.
- People preferring both Folk and Rock, but not Jazz: 35.
- Total people listening to exactly two genres: 130.
- So, 35 + 50 + 0.75x = 130 ? 85 + 0.75x = 130 ? x = 60.
- From the equation given for only Jazz: J = 6 * 35 - 5 = 205.
- We know the ratio and can find F and R by setting up equations:
- F / 56 = R / 79 = J / 41 = k. Substitute J = 205 to get k.
- k = 205 / 41 = 5.
- F = 5 * 56 = 280.
- R = 5 * 79 = 395.
- Total for only Folk and only Rock: 280 (Folk) + 395 (Rock) = 675.
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