document.write( "Question 264383: A class of 30 music students includes 13 who play the piano, 16 who play
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Algebra.Com's Answer #194644 by Edwin McCravy(20056) $\"\"$ $\"About$

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A class of 30 music students includes 13 who play the piano, 16 who play
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document.write( "We will draw what is called a \"Venn diagram\":\r\n" );
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document.write( "Imagine you have all 30 students on a football field.\r\n" );
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document.write( "First draw a big rectangle to represent, say, the big football field, \r\n" );
document.write( "for all 30 music students to stand on.\r\n" );
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document.write( "Now on that football field draw a big circle for the 13 students\r\n" );
document.write( "to stand in who play piano and label it P:\r\n" );
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document.write( "Next draw another big circle overlapping it for the 16 students\r\n" );
document.write( "to stand in who play the guitar and label it G:\r\n" );
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document.write( "Now we tell the 5 students who like both both instruments to stand\r\n" );
document.write( "in the overlapping part of those two circles.  So we'll write  \r\n" );
document.write( "in there to represent the 5 students in that region.  Those 5 have to\r\n" );
document.write( "stand in BOTH CIRCLES at the same time! The way to stand in both\r\n" );
document.write( "circles at the same time is to stand in the overlapping part of the\r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Since there are 13 students who play the piano, the rest of those 13 \r\n" );
document.write( "besides the 5 that like both piano and guitar, that is, 13-5, or 8, \r\n" );
document.write( "will have to stand in this region, in which we write 8:\r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Since there are 16 students who play guitar, the rest of those 16 \r\n" );
document.write( "besides the 5 that like both, that is, 16-5, or 11, will have to \r\n" );
document.write( "stand in this region, in which we write 11:\r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Now we have accounted for 8 + 5 + 11 or 24 of the 30 students.  That\r\n" );
document.write( "leaves 30-24, or 6 students who play neither instrument, and so \r\n" );
document.write( "those 6 have to stand outside the two circles, like this:\r\n" );
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document.write( "So the answer is 6.\r\n" );
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document.write( "Edwin

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