document.write( "Question 1106293: In a class of 60 students, the number of students who passed Biology is 6 more than the number of students who passed Chemistry. Every student passed at least one of the two subjects and 8 students passed both subjects. a. illustrate this information on a venn diagram. b. How many students passed i. chemistry ii. Biology iii. only chemistry iv. only Biology Find the percentage of the students who passed exactly one subject only \n" ); document.write( "

Algebra.Com's Answer #721278 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Let me show you how to solve the problem WITHOUT using a Venn diagram.\r
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document.write( "Let B be the number of students who passed the Biology   exam only.\r\n" );
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document.write( "Let C be the number of students who passed the Chemistry exam only.\r\n" );
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document.write( "Then your first equation is  \r\n" );
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document.write( "B + C + 8 = 60      (1)    (\"Every student passed at least one of the two subjects and 8 students passed both subjects.\")\r\n" );
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document.write( "Your second equation is \r\n" );
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document.write( "(B+8) - (C+8) = 6   (2)    (\"the number of students who passed Biology is 6 more than the number of students who passed Chemistry\")\r\n" );
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document.write( "Simplify equations (1) and (2). You will get\r\n" );
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document.write( "B + C = 52,          (1')\r\n" );
document.write( "B - C =  6.          (2')\r\n" );
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document.write( "Now add equations (1) and (2). You will get\r\n" );
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document.write( "2B = 52 + 6 = 58  ====>  B =  = 29.\r\n" );
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document.write( "Then  from (1')  C = 52 - 29 = 23.\r\n" );
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document.write( "Answer.  29 students passed Biology only.\r\n" );
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document.write( "         23 students passed Chemistry only.\r\n" );
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document.write( "         29+8 = 37 passed Biology   (of them, 8 passed both).\r\n" );
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document.write( "         23+8 = 31 passed Chemistry (of them, 8 passed both).\r\n" );
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