document.write( "Question 1191509: A group of office workers had some prize money to distribute among themselves. When all but one took $9 each, the last person only received $5. When they all took $8 each, there was $12 left over. How much had they won? \n" ); document.write( "

Algebra.Com's Answer #823299 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "A group of office workers had some prize money to distribute among themselves.
\n" ); document.write( "When all but one took $9 each, the last person only received $5.
\n" ); document.write( "When they all took $8 each, there was $12 left over. How much had they won?
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document.write( "Let n be the number of workers.\r\n" );
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document.write( "We can express the total money in two different ways.\r\n" );
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document.write( "One way is      the total money = 9*(n-1) + 5\r\n" );
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document.write( "Another way is  the total money = 8*n + 12.\r\n" );
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document.write( "Since the total money is the same,\r\n" );
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document.write( "    9*(n-1) + 5 = 8n + 12\r\n" );
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document.write( "Simplify and find n\r\n" );
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document.write( "    9n - 9 + 5 = 8n + 12\r\n" );
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document.write( "    9n - 4 = 8n + 12\r\n" );
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document.write( "    9n - 8n = 12 + 4\r\n" );
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document.write( "       n    =   16.\r\n" );
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document.write( "So, there are 16 workers, and the total prize money is  8n+12 = 8*16 + 12 = 140 dollars.    ANSWER\r\n" );
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