document.write( "Question 940201: out of 70 students, 38 own a radio and 28 own a TV. If 8 students don't own either of them, what fraction of the students owns both a radio and TV? \n" ); document.write( "

Algebra.Com's Answer #572999 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "I think your teacher wants you to use a Venn diagram (also known as Euler\r\n" );
document.write( "diagram) like this:\r\n" );
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document.write( "The red circle represents a set R that contains all those who own a radio.\r\n" );
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document.write( "The blue circle represents a set T that contains all those who own a TV.\r\n" );
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document.write( "The left region of the red circle that has \"a\" in it are those who own\r\n" );
document.write( "a Radio but do not own a TV.  \r\n" );
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document.write( "The middle region that has a \"b\" is part of both circles, and represents \r\n" );
document.write( "a set that contains all those who own BOTH a radio and a TV.\r\n" );
document.write( "The right region of the blue circle that has \"c\" in it are those who own\r\n" );
document.write( "a TV but do not own a radio.\r\n" );
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document.write( "The region that has \"d\" in it is outside of both circles.  It represents\r\n" );
document.write( "the ones which have neither a radio nor a TV.  \r\n" );
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\n" ); document.write( "If 8 students don't own either of them,
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document.write( "Therefore d=8, so we replace d by 8\r\n" );
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\n" ); document.write( "38 own a radio
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document.write( "Therefore a+b=38\r\n" );
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\n" ); document.write( "and 28 own a TV.
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document.write( "Therefore b+c=28\r\n" );
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\n" ); document.write( "out of 70 students,
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document.write( "Therefore a+b+c+d=70, and since d=8,\r\n" );
document.write( "a+b+c+8=70 or a+b+c=62\r\n" );
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document.write( "Subtracting these equations:\r\n" );
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document.write( "a+b+c=62\r\n" );
document.write( "a+b  =38\r\n" );
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document.write( "    c=24\r\n" );
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document.write( "Substituting in b+c=28\r\n" );
document.write( "   b+24=28\r\n" );
document.write( "      b=4\r\n" );
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document.write( "Substituting in \r\n" );
document.write( "    a+b=38\r\n" );
document.write( "    a+4=38\r\n" );
document.write( "      a=34\r\n" );
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document.write( "So the complete Venn diagram is\r\n" );
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\n" ); document.write( "what fraction of the students owns both a radio and TV
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document.write( "That's the 4 in the middle region.\r\n" );
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document.write( "4 out of 70 is the fraction .\r\n" );
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document.write( "Edwin

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