document.write( "Question 318985: Cheryl of Cheryl's bakery set out 18 cups of flour, 14 cups of sugar, and 13 cups of shortening for her employees to use and make some batches of chocolate chip cookies, oatmeal and peanut butter cookies. She left for the day without telling them how many batches of each type of cookie to bake. the table below gives the number of cups and ingredients required for one batch of each cookie, how many batches of each cookie type were supposed to be baked?
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Algebra.Com's Answer #228336 by Edwin McCravy(20086) $\"\"$ $\"About$

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Cheryl of Cheryl's bakery set out 18 cups of flour, 14 cups of sugar, and 13 cups of shortening for her employees to use and make some batches of chocolate chip cookies, oatmeal and peanut butter cookies. She left for the day without telling them how many batches of each type of cookie to bake. the table below gives the number of cups and ingredients required for one batch of each cookie, how many batches of each cookie type were supposed to be baked?
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document.write( "    Flr Sug Sho       \r\n" );
document.write( "CC-  2   2   1\r\n" );
document.write( "O -  1   1   2   matrix rows are: choco chip,otm, peaunt b, \r\n" );
document.write( "PB-  4   2   1   matrix coloums : flour, sugar, shortening\r\n" );
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document.write( "SOLVE USING CRAMER'S RULE\r\n" );
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document.write( "(Cramer's rule does not lead to a solution if the determinant of coefficients\r\n" );
document.write( "is 0.)\r\n" );
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document.write( "The question asks:\r\n" );
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document.write( ">>...how many batches of each cookie type were supposed to be baked?...<<\r\n" );
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document.write( "Let x = the number of batches of chocolate chip cookies,\r\n" );
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document.write( "Let y = the number of batches of oatmeal cookies,\r\n" );
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document.write( "Let z = the number of batches of peanut butter cookies\r\n" );
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document.write( "Then \r\n" );
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document.write( "1.  We make the \"flour\" equation:\r\n" );
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document.write( "2x + 1y + 4z = 18\r\n" );
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document.write( "2.  We make the \"Sugar\" equation:\r\n" );
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document.write( "2x + 1y + 2z = 14\r\n" );
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document.write( "3.  We make the \"shortening\" equation:\r\n" );
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document.write( "1x + 2y + 1z = 13\r\n" );
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document.write( "So we have the system:\r\n" );
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document.write( "To Form the denominator determinant  from the \r\n" );
document.write( "coefficients of the letters:\r\n" );
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document.write( "However that determinant is 0 which tells us that Cramer's rule\r\n" );
document.write( "cannot be used and the the system is either dependent or\r\n" );
document.write( "inconsistent. \r\n" );
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document.write( "Form the determinant  by copying the red numbers in place of the\r\n" );
document.write( "first column:\r\n" );
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document.write( "Form the determinant  by copying the red numbers in place of the\r\n" );
document.write( "second column:\r\n" );
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document.write( " which when evaluated gives  by copying the red numbers in place of the\r\n" );
document.write( "second column:\r\n" );
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document.write( "Expanding the matrices, we get , , , and \r\n" );
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document.write( "The formulas for x, y, and z are:\r\n" );
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document.write( "So the system is inconsistent.\r\n" );
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document.write( "Edwin

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