document.write( "Question 1143524: Matt brought several cartons of large eggs for $112. If he had bought extra-large eggs costing $1 more per carton, he would have 2 less cartons of eggs for the same money. How much did he pay for a carton of large eggs? \n" ); document.write( "

Algebra.Com's Answer #764353 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " I will show you another way to solve the problem using only one unknown from the very beginning.\r
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document.write( "Let x be the price for a carton of large eggs (the unknown value under the question).\r\n" );
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document.write( "Then Matt bought    cartoons of large eggs.\r\n" );
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document.write( "The price extra-large eggs is then  (x+1) dollars per cartoons, so he could buy    cartoons of extra-large eggs.\r\n" );
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document.write( "The condition says that\r\n" );
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document.write( "     -  = 2.\r\n" );
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document.write( "The setup is completed.\r\n" );
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document.write( "To solve the equation, multiply both sides by x*(x+1).\r\n" );
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document.write( "    112*(x+1) - 112x = 2x*(x+1)\r\n" );
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document.write( "    112x + 112 - 112x = 2x^2 + 2x\r\n" );
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document.write( "    2x^2 + 2x - 112 = 0\r\n" );
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document.write( "    x^2 + x - 56 = 0\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (x-7)*(x+8) = 0\r\n" );
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document.write( "It has two roots, but only positive root  x= 7  makes sense.\r\n" );
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document.write( "ANSWER.  The price of a cartoon of large eggs is $7.\r\n" );
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document.write( "CHECK.   At $7 per cartoon, Matt bough   = 16 cartoons of large eggs.\r\n" );
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document.write( "         At the price (7+1) = 8 dollars per cartoon, Matt could buy   = 14 cartoons of extra-large eggs.\r\n" );
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document.write( "         The difference is 16-14 = 2, in accordance with the condition  (!)\r\n" );
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\n" ); document.write( "\n" ); document.write( "You can solve the problem by EITHER of the two ways.\r
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\n" ); document.write( "\n" ); document.write( "If you want to see other similar solved problems, look into the lesson\r
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