document.write( "Question 766596: In a survey of a TriDelt chapter with 50 members, 21 were taking mathematics, 36 were taking English, and 9 were taking both. How many were not taking either of these subjects?
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Algebra.Com's Answer #467117 by Edwin McCravy(20055)\"\" \"About 
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In a survey of a TriDelt chapter with 50 members, 21 were taking mathematics, 36 were taking English, and 9 were taking both. How many were not taking either of these subjects?
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document.write( "We draw a rectangle with two overlapping circles, one red and one blue.\r\n" );
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document.write( "There are two circles.  The red one contains all the students taking\r\n" );
document.write( "math.  The blue one contains all the students taking English.  Note\r\n" );
document.write( "that the red circle and the blue circle overlap.  \r\n" );
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document.write( "Here is the mistake many students make, so DO NOT make this\r\n" );
document.write( "mistake:\r\n" );
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document.write( "Many students would see the words \"21 were taking mathematics,36 were taking English,\",\r\n" );
document.write( "and put all 21 in region \"a\", and all 36 in region \"c\", like this:\r\n" );
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document.write( "DO NOT make that error!!! Some, but not all, of the 21 go in\r\n" );
document.write( "region \"a\" and the rest of the go in region \"b\".  Similar,\r\n" );
document.write( "Some, but not all, of the 36 go in region \"d\" and the rest \r\n" );
document.write( "of the go in region \"b\".\r\n" );
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document.write( "So we do not begin with either the 21 or the 36. \r\n" );
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document.write( " Instead we begin with  \"9 were taking both\".  These 9 go in\r\n" );
document.write( "the middle region, b, because those 9 are in both the red\r\n" );
document.write( "circle and the blue circle.\r\n" );
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document.write( "So we put the 9 in region b:\r\n" );
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document.write( "Now we see \"21 were taking mathematics\", and of this 21,\r\n" );
document.write( "9 are taking English too, so we must subtract the 9\r\n" );
document.write( "that are in the middle region, getting 21-9 = 12, and\r\n" );
document.write( "we put 12 in region \"a\":\r\n" );
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document.write( "Now we see \"36 were taking English\", and of this 36,\r\n" );
document.write( "9 are taking  too, so we must subtract the 9\r\n" );
document.write( "that are in the middle region, getting 36-9 = 27, and\r\n" );
document.write( "we put 27 in region \"c\":\r\n" );
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document.write( "We have one more region, \"d\".  That is the region\r\n" );
document.write( "outside of both circles.  They are the ones that are neither\r\n" );
document.write( "taking mathematics nor taking English.\r\n" );
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document.write( "We have accounted for 12+9+27 = 48.  We are told there are 50\r\n" );
document.write( "members. So there are 50-48 = 2 that have not been accounted\r\n" );
document.write( "for.  Those 2 go in the outer region \"d\":\r\n" );
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document.write( "So the answer to the problem is those 2.\r\n" );
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document.write( "Edwin
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