document.write( "Question 1021884: A company has 22 employees. Twelve of these
\n" ); document.write( "employees have masters degrees and fifteen
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\n" ); document.write( "How many have both a Masters degree and a
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Algebra.Com's Answer #637854 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Everybody in the red circle M have masters.\r\n" );
document.write( "Everybody in the blue circle C have certification.\r\n" );
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document.write( "a = the number of employees who have a masters but no certification\r\n" );
document.write( "b = the number of employees who have both a masters and a certification\r\n" );
document.write( "c = the number of employees who have a certification but no masters\r\n" );
document.write( "d = the number of employees who have neither a masters nor a \r\n" );
document.write( "certification\r\n" );
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A company has 22 employees.

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document.write( "a+b+c+d = 22

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document.write( "a+b = 12

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document.write( "b+c = 15

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document.write( "d = 3\r\n" );
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document.write( "So we have this system of four equations and 4 unknowns:\r\n" );
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document.write( "Solve by substitution or elimination.\r\n" );
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document.write( "Subtract the 2nd equation from the first, get c+d=10.\r\n" );
document.write( "Substitute d=3, get c=7.  Substitute c=7 in b+c=15,\r\n" );
document.write( "get b=8.  Substitute b=8 in a+b=12, get a=4.

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document.write( "That's b = 8.\r\n" );
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document.write( "Edwin

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