document.write( "Question 261801: In a certain club, 14 members speak Spanish, 7 members speak Creole and 4 members speak both Creole or Spanish, and 37 members speak neither Creole nor Spanish. Find the numbers of members in this club. \n" ); document.write( "

Algebra.Com's Answer #192904 by Edwin McCravy(20064) $\"\"$ $\"About$

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In a certain club, 14 members speak Spanish, 7 members speak Creole and 4 members speak both Creole or Spanish, and 37 members speak neither Creole nor Spanish. Find the numbers of members in this club.\r
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document.write( "You can do this either by a Venn diagram or by a formula.\r\n" );
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document.write( "I'll first do it by a Venn diagram and then I'll do it\r\n" );
document.write( "using a formula.\r\n" );
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document.write( "VENN DIAGRAM METHOD:\r\n" );
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document.write( "Imagine you have all the members in the bleachers of football field.\r\n" );
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document.write( "First draw a big rectangle to represent, say, a big football field,\r\n" );
document.write( "for all the club members to come down and stand in.\r\n" );
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document.write( "Now on that football field draw a big circle for all 14 members\r\n" );
document.write( "to stand in who speak Spanish and label it S:\r\n" );
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document.write( "Next draw another big circle overlapping it for all 7 members\r\n" );
document.write( "to stand in who speak Creole and label it C:\r\n" );
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document.write( "Now the 37 members who speak neither Creole nor Spanish will have \r\n" );
document.write( "to stand on the field outside both circles, so we'll write 37 out \r\n" );
document.write( "there to stand for the 37 students who will stand out there:\r\n" );
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document.write( "The 4 members who speak both Creole and Spanish will be standing \r\n" );
document.write( "in both circles, that is, they will be standing in the overlapping \r\n" );
document.write( "part of the two circles, so we'll write 4 in the overlapping part\r\n" );
document.write( "to stand for the 4 members who will stand there.\r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Since there are 14 members who speak Spanish, the rest of those 14\r\n" );
document.write( "besides the 4 that speak both languages, that is, 14-4, or 10, will \r\n" );
document.write( "have to stand in this region, in which we write 10:\r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Since there are 7 members who speak Creole, the rest of those 7\r\n" );
document.write( "besides the 4 that speak both languages, that is, 7-4, or 3, will\r\n" );
document.write( "have to stand in this region, in which we write 3:\r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Now we add up all the numbers in the four regions and\r\n" );
document.write( "that sum must be all the club members standing somewhere\r\n" );
document.write( "on the football field:\r\n" );
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document.write( "37+10+4+3 = 54\r\n" );
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document.write( "The answer is: There are 54 members in the club.\r\n" );
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document.write( "FORMULA METHOD:\r\n" );
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document.write( "N(S or C) = N(S) + N(C) - N(S and C)\r\n" );
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document.write( "N(S or C) = 14 + 7 - 4\r\n" );
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document.write( "N(S or C) = 17\r\n" );
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document.write( "Now the total number of members in the club =\r\n" );
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document.write( "N(S or C) + N[not(S or C)]\r\n" );
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document.write( "17 + 37 = 54 members in the club\r\n" );
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document.write( "Edwin

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