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 December 3rd, 2011, 12:34 AM #1 Newbie   Joined: Dec 2011 Posts: 4 Thanks: 0 Sets helps.... In a survey of 120 people, 48 Played basketball , 78 Played Soccer, 66 Played Volleyball, 36 Played any given pair of these sports , 24 Played them all. Find the number of the people that played at least one of the sports..
 December 3rd, 2011, 12:44 PM #2 Global Moderator   Joined: May 2007 Posts: 6,584 Thanks: 611 Re: Sets helps.... Set up a Venn diagram.
 December 3rd, 2011, 03:32 PM #3 Newbie   Joined: Dec 2011 Posts: 4 Thanks: 0 Re: Sets helps.... venn diagram is no problem for me...but i still cnt find the actual answer...
 December 3rd, 2011, 04:37 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 Math Focus: Calculus/ODEs Re: Sets helps.... Let: a = # that play basketball only b = # that play soccer only c = # that play volleyball only x = # that play basketball and soccer y = # that play basketball and volleyball z = # that play soccer and volleyball We are told: x + y + z = 36 a + x + y + 24 = 48 b + x + z + 24 = 78 c + y + z + 24 = 66 Adding, we find: (a + b + c) + 3(x + y + z + 24) = 228 (a + b + c) + (x + y + z + 24) = 228 - 2(x + y + z + 24) (a + b + c) + (x + y + z) + 24 = 228 - 2(36 + 24) = 108 This expression represents the number of people who play at least one of the given sports.
December 3rd, 2011, 05:17 PM   #5
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From: Lexington, MA

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Re: Sets helps....

Hello, dannyboyz!

Quote:
 In a survey of 120 people: [color=beige]. . [/color]48 played Basketball. [color=beige]. . [/color]78 played Soccer. [color=beige]. . [/color]66 played Volleyball. [color=beige]. . [/color]36 played Basketball and Soccer. [color=beige]. . [/color]36 played Soccer and Volleyball. [color=beige]. . [/color]36 played Basketball and Volleyball. [color=beige]. . [/color]24 played all three sports. Find the number of the people that played at least one of the sports.

Are you familiar with this formula?

$n(B\,\!\cup\,\!S\,\!\cup\,\!V) \:=\:n(B)\,+\,n(S)\,+\,n(V)\,-\,n(B\,\!\cap\,\!S)\,-\,n(S\,\!\cap\,\!V) \,-\,n(B\,\!\cap\,\!V)\,+\,n(B\,\!\cap\,\!S\,\!\cap\, \!V)$

 December 4th, 2011, 05:15 AM #6 Newbie   Joined: Dec 2011 Posts: 4 Thanks: 0 Re: Sets helps.... thx for the reply..i also find that the answer is 108... I am confuse tat why my tutor say the answer is wrong ==
 December 4th, 2011, 09:06 AM #7 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 Math Focus: Calculus/ODEs Re: Sets helps.... How does your tutor work the problem?
 December 4th, 2011, 11:07 PM #8 Newbie   Joined: Dec 2011 Posts: 4 Thanks: 0 Re: Sets helps.... Today i go and ask my tutor again..she said...the answer is not wrong ==

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