document.write( "Question 1131150: A carpenter earned $720 for a certain job. Her apprentice also earned $720, but the apprentice earned $6 less per hour and worked 10 hours more than the carpenter. How much did the carpenter earn per hour? \n" ); document.write( "

Algebra.Com's Answer #747807 by ikleyn(52777) $\"\"$ $\"About$

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document.write( "Let x = the carpenter's hourly rate (in dollars), and h = time in hours the carpenter worked.\r\n" );
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document.write( "Then the apprentice's hourly rate is (x-6) dollars, and his (or her (?)) working time is (h+10) hours.\r\n" );
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document.write( "Then from the condition, you have this system of equations\r\n" );
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document.write( "    x*h = 720,              (1)\r\n" );
document.write( "    (x-6)*(h+10) = 720      (2)\r\n" );
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document.write( "To solve the system, first FOIL equation (2). You will get\r\n" );
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document.write( "    xh - 6h + 10x - 60 = 720.    (3)\r\n" );
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document.write( "In (3), replace xh by 720, based on (1).  You will get\r\n" );
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document.write( "    720 - 6h + 10x - 60 = 720,   which is simplified to\r\n" );
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document.write( "    10x - 6h = 60.               (4)\r\n" );
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document.write( "Write equation (1) as  \r\n" );
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document.write( "    6xh = 6*720;                 (5)\r\n" );
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document.write( "from equation (4), express 6h = 10x - 60  and substitute it into equation (5).  You will get\r\n" );
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document.write( "    (10x - 60)*x = 6*720,\r\n" );
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document.write( "    10x^2 - 60x + 6*720 = 0,\r\n" );
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document.write( "    x^2 - 6x + 6*72 = 0,\r\n" );
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document.write( "    (x-24)*(x+18) = 0.\r\n" );
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document.write( "Of two solutions  x= 24  and  x= -18,  only positive solution  x= 24  is meaningful, giving the\r\n" );
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document.write( "ANSWER.  The carpenter's hourly rate is  $24 per hour.\r\n" );
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document.write( "CHECK.   The carpenter's working time is  h= 720/24 = 30 hours.\r\n" );
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document.write( "         The apprentice's hourly rate is  $24 - $6 = $18 and his (or her (?) ) working time is  30+10 = 40 hours.\r\n" );
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document.write( "         Both products  24*30  and  18*40  are equal to 720  dollars.   ! Correct !\r\n" );
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