document.write( "Question 1191077: Normally a factory produces 400 radios in x days. IF the factory were to produce 20 more radios each day, then it would take 10 days less to produce 400 radios. find x \n" ); document.write( "

Algebra.Com's Answer #822830 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "Normally a factory produces 400 radios in x days.
\n" ); document.write( "IF the factory were to produce 20 more radios each day, then it would take 10 days less to produce 400 radios.
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document.write( "Producing x items per day, it will take    days to make 400 items.\r\n" );
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document.write( "Producing (x+20) items each day, it will take    days to make 400 items.\r\n" );
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document.write( "The difference   -   is 10 days, according to the problem.\r\n" );
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document.write( "So we have this \"time\" equation\r\n" );
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document.write( "     -  = 10   days.      (1)\r\n" );
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document.write( "Dividing both sides by 10 gives\r\n" );
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document.write( "     -  = 1.\r\n" );
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document.write( "At this point, you may guess the solution MENTALLY:  it is  x = 20.\r\n" );
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document.write( "Alternatively, you may reduce it to the quadratic equation and solve it formally.\r\n" );
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document.write( "For it, multiply both sides by x*(x+20).  You will get\r\n" );
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document.write( "    40*(x+20) + 40*x = x*(x+20)\r\n" );
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document.write( "    40x + 800 - 40x = x^2 + 20x\r\n" );
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document.write( "    x^2 + 20x - 800 = 0\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (x-20)*(x+40) = 0\r\n" );
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document.write( "Of the two roots, 20 and -40, we disregard the negative root  x= -40  and accept the positive root x= 20.    ANSWER\r\n" );
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document.write( "CHECK.  We will check the starting equation (1)\r\n" );
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document.write( "         -  =  -  = 20 - 10 = 10  days.    ! Correct !\r\n" );
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