document.write( "Question 1123099: Solve By Elimination:
\n" ); document.write( "Roast beef has 25 grams of protein and 11 grams of calcium per serving. A serving of mashed potatoes has 2 grams of protein and 25 grams of calcium. How many servings of each are needed to supply exactly 29 grams of protein and 61 grams of calcium? Use b for servings of beef and m for servings of mashed potatoes. \n" ); document.write( "

Algebra.Com's Answer #739329 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "25*b +  2*m = 29    grams of protein   (1)\r\n" );
document.write( "11*b + 25*m = 61    grams of calcium   (2)\r\n" );
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document.write( "Multiply eq(1) by 25 (both sides);  multiply eq(2) by 2 (both sides). You will get\r\n" );
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document.write( "25*25*b + 50*m = 25*29    (3)\r\n" );
document.write( " 2*11*b + 50*m =  2*61    (4)\r\n" );
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document.write( "Subtract eq(4) fro eq(3). You will get\r\n" );
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document.write( "25*25*b - 2*11*b = 25*29-2*61,   or\r\n" );
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document.write( "(25*25 - 2*11)*b = 25*29 - 2*61\r\n" );
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document.write( "b =  = 1.    (*)  <<<---=== I specially / (intently) did not make intermediate calculations until I got this formula.\r\n" );
document.write( "                                      Then I copied the formula to Excel spreadsheet in my computer and calculated it \"in one click\".\r\n" );
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document.write( "Thus you just found \"b\" by elimination.\r\n" );
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document.write( "Now from eq(1),  m =  = 2.\r\n" );
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document.write( "Answer.  b= 1,  m= 2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you just know the determinant method (which is the same as the Cramer's rule),
\n" ); document.write( "you will easily recognize that the denominator in the formula (*) is the determinant of the coefficient matrix
\n" ); document.write( "to equations (1) and (2), while the numerator is the determinant of the modified matrix by the Cramer's rule.\r
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\n" ); document.write( "\n" ); document.write( "When you use the Elimination method, it is an additional way to check that all your actions are / were correct.\r
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