document.write( "Question 1164247: Some mathematics professors would like to purchase a $140 microwave oven for the department workroom. If 5 of the professors do not contribute, everyone's share will increase by $50. How many professors are in the department? \n" ); document.write( "
Algebra.Com's Answer #788540 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "OH CRAP!!!  Ikleyn did it for you before I could post this!\r\n" );
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document.write( "Instead of doing your problem for you, I'll do one EXACTLY like yours so\r\n" );
document.write( "that you can use it as a model for your problem:\r\n" );
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document.write( "Some mathematics professors would like to purchase a $300 microwave oven for\r\n" );
document.write( "the department workroom. If 6 of the professors do not contribute,\r\n" );
document.write( "everyone's share will increase by $45. How many professors are in the\r\n" );
document.write( "department? \r\n" );
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document.write( "If all N professors shared, then everyone's share would be 300/N\r\n" );
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document.write( "If 6 professors do not contribute, the share for the N-6 professors who do\r\n" );
document.write( "contribute will be $45 more than that or $(300/N + 45)\r\n" );
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document.write( "So the equation is:\r\n" );
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document.write( "(N-6)(300/N+45) = 300\r\n" );
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document.write( "Use FOIL to multiply that out:\r\n" );
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document.write( "N(300/N) + 45N - 1800/N + 270 = 300\r\n" );
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document.write( "     300 + 45N - 1800/N + 270 = 300\r\n" );
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document.write( "           45N - 1800/N + 270 = 0\r\n" );
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document.write( "Multiply through by N to clear the fraction:\r\n" );
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document.write( "           45N² - 1800 + 270N = 0\r\n" );
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document.write( "           45N² + 270N - 1800 = 0\r\n" );
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document.write( "Divide through by 45\r\n" );
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document.write( "                 N² + 6N - 40 = 0 \r\n" );
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document.write( "Factor         (N - 10)(N + 4) = 0\r\n" );
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document.write( "             N - 10 = 0; N + 4 = 0\r\n" );
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document.write( "                 N = 10;    N = -4\r\n" );
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document.write( "N = 10 professors.  Ignore the negative answer.\r\n" );
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document.write( "Now use this as a model to do yours.\r\n" );
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document.write( "Edwin
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