document.write( "Question 1089553: Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 109 g protein, 103 g fat, and 153 g carbohydrate. According to the health conscious hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, and 6 g carbohydrate. How many of each snack can he eat to obtain his goal? \n" ); document.write( "

Algebra.Com's Answer #703902 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to
\n" ); document.write( "109 g protein, 103 g fat, and 153 g carbohydrate.
\n" ); document.write( "According to the health conscious hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate;
\n" ); document.write( "the spicy meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate;
\n" ); document.write( "and the deviled eggs have 13 g protein, 15 g fat, and 6 g carbohydrate.
\n" ); document.write( "How many of each snack can he eat to obtain his goal?
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document.write( "Let x be the number of the marinated mushroom caps;\r\n" );
document.write( "    y be the number of the spicy meatball;\r\n" );
document.write( "    z be the number of the deviled eggs.\r\n" );
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document.write( "According to the condition, these tree balance equations are in place:\r\n" );
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document.write( "   3x + 14y + 13z = 109  grams of protein         (1)\r\n" );
document.write( "   5x +  7y + 15z = 103  grams of fat             (2)\r\n" );
document.write( "   9x + 15y +  6z = 153  grams of carbohydrate    (3)\r\n" );
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document.write( "So, what Ron must do is to input the coefficients of the matrix and the right side terms into his calculator and then press the button .\r\n" );
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document.write( "Then he will obtain the answer.\r\n" );
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document.write( "Instead of calculator, I used this popular free of charge online solver in this site\r\n" );
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document.write( "https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver\r\n" );
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document.write( "written by our colleague  Jim Thompson to get this answer:\r\n" );
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document.write( "x = 9   (marinated mushroom caps),\r\n" );
document.write( "y = 4   (spicy meatball),\r\n" );
document.write( "z = 2   (deviled eggs).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( " B o n e a p p e t i t e s ! !\r
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