document.write( "Question 1157583: A class has 30 students. 21 students like math and 9 like english . If 16 students like math only and 5 students like neither math nor English, how many students like both math and English? Draw a Venn diagram to represent the information. \n" ); document.write( "
Algebra.Com's Answer #780811 by Edwin McCravy(20056)\"\" \"About 
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A class has 30 students. 21 students like math and 9 like english . If 16 students like math only and 5 students like neither math nor English, how many students like both math and English? Draw a Venn diagram to represent the information.
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document.write( "Everybody in the red circle likes math.\r\n" );
document.write( "Everybody in the blue circle likes English.\r\n" );
document.write( "a = the number who like math only\r\n" );
document.write( "b = the number who like both math and English.\r\n" );
document.write( "c = the number who like English only.\r\n" );
document.write( "d = the number who do not like either math or English.\r\n" );
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document.write( "A class has 30 students.  So a+b+c+d = 10\r\n" );
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document.write( "21 students like math. So a+b = 21 \r\n" );
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document.write( "9 like English.  So b+c = 9\r\n" );
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document.write( "16 students like math only.  So a = 16 \r\n" );
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document.write( "5 students like neither math nor English.  So d = 5 \r\n" );
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how many students like both math and English?
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document.write( "Since 21 like math of which 16 like math only, the other 5 must like both math\r\n" );
document.write( "and English.  So we have the answer immediately, 5 like both.\r\n" );
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document.write( "Draw a Venn diagram to represent the information.\r\n" );
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document.write( "a=16, b=5 (which is the answer).\r\n" );
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document.write( "We have everything in the Venn diagram except c. But since 9 like English,\r\n" );
document.write( "and since 5 like both, the other 4 must like English only. So c = 4.\r\n" );
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document.write( "We didn't need to be told that there are 30 students.  We could have figured\r\n" );
document.write( "that out just by adding 16+5+4+5 = 30. \r\n" );
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document.write( "Edwin

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