document.write( "Question 1115665: If a beet-sugar factory in England processed 2000 tons less of beets per day, it would take 1 day longer to slice 60,000 tons of them. How many tons of beets are processed per day? \n" ); document.write( "

Algebra.Com's Answer #730524 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let x = \"How many tons of beets are processed per day?\", i.e. the value under the question.\r\n" );
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document.write( "Then the condition gives you this equation\r\n" );
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document.write( "     -  = 1,     (1)\r\n" );
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document.write( "which is direct translation of the condition to Math.\r\n" );
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document.write( "To simplify calculations, we can make an agreement that we measure the amounts not in tons, but in THOUSANDS of tons.\r\n" );
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document.write( "Then the equation (1) takes the form\r\n" );
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document.write( "     -  = 1.              (2)\r\n" );
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document.write( "Then I can solve it mentally:  x = 12.\r\n" );
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document.write( "Indeed,   -  =  = 6 - 5 = 1.\r\n" );
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document.write( "You can solve the equation (2) formally by multiplying both sides by x:\r\n" );
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document.write( "60*x - 60*(x-2) = x*(x-2),\r\n" );
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document.write( "60x - 60x + 120 = x^2 - 2x\r\n" );
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document.write( "x^2 - 2x - 120 = 0\r\n" );
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document.write( "(x - 12)*(x + 10) = 0.\r\n" );
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document.write( "Of the two roots  x= 12  and  x= -10  only positive root x= 12 satisfies the condition.\r\n" );
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document.write( "Answer.  12000 tons of beets are processed per day normally.\r\n" );
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