document.write( "Question 1132635: A business director awards his staff with gift cards of $10.00 value each. He gives 3 gift cards to employees who have been employed in his business for 3 years, 5 gift cards to employees who have worked there for 5 years, and 10 gift cards for employees working there for 10 years. He gives out a total of 282 gift cards.\r
\n" ); document.write( "\n" ); document.write( "He has 14 more employees that working there for 3 years, than for 5 years. Also there are 3 fewer employees who have been working there for 10 years than for 5 years.\r
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Algebra.Com's Answer #749729 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "3x + 5y + 10z = 282    (1)  (counting the cards)\r\n" );
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document.write( "where x, y and z are the corresponding numbers of employees.\r\n" );
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document.write( "Two additional equations, from the condition, are\r\n" );
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document.write( "x - 14 = y             (2)\r\n" );
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document.write( "y - 3 = z              (3)\r\n" );
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document.write( "Now you can express  y = z+3  from  (3),  and  x = y+14 = (z+3) + 14 = z + 17 from (2) and (3).  Substitute it into eq(1) to get\r\n" );
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document.write( "3*(z+17) + 5*(z+3) + 10z = 282.\r\n" );
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document.write( "Simplify and solve for z\r\n" );
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document.write( "3z + 51 + 5z + 15 + 10z = 282,\r\n" );
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document.write( "18z + 66 = 282,\r\n" );
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document.write( "18z = 282 - 66 = 216  ====>  z = 216/18 = 12.\r\n" );
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document.write( "ANSWER.  12 employees have been working there for 10 years.\r\n" );
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