SOLUTION: In a survey of 260 dancers, 172 knew the ballroom dances, 145 knew the Latin dances, and 102 knew the swing dances. Of these, 65 knew the ballroom and swing dances, 93 knew the bal

Question 433209: In a survey of 260 dancers, 172 knew the ballroom dances, 145 knew the Latin dances, and 102 knew the swing dances. Of these, 65 knew the ballroom and swing dances, 93 knew the ballroom and Latin dances, and 56 knew the Latin and swing dances. Thirty-one dancers indicated that they knew all three styles of dance.

(a) How many knew only the ballroom dances?
(b) How many knew only the swing dances?
(c) How many knew exactly two of the three dances?
(d) How many knew the Latin and swing dances, but not the ballroom dances?
(e) How many knew none of these dances?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
I solve this type of problem by drawing
a Venn diagram and then I find how many
are in each little section of it.
B = ballroom
L = Latin
S = Swing
B and S but not other dances = 65 - 31 = 34
B and L but not other dances = 93 - 31 = 62
L and S but not other dances = 56 - 31 = 25
--------------
Now I can identify
B DISABLED_event_only= 172 - (34 + 62 + 31) = 45
L DISABLED_event_only= 145 - (62 + 31 + 25) = 27
S DISABLED_event_only= 102 - (34 + 31 + 25) = 12
--------------
(a) 45
(b) 12
(c) 34 + 62 + 25 = 121
(d) 25
(e) Counting each area only once,
45 + 27 + 12 + 34 + 62 + 25 + 31 = 236
260 - 236 = 24

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