document.write( "Question 1194016: A dietitian wishes to plan a meal around three foods: The percentages of the daily requirements carbohydrates, and iron contained in each ounce of the protein. three foods are summarized in the following table:
\n" ); document.write( " Food I Food II Food III
\n" ); document.write( "Protein (%) 10 6 8
\n" ); document.write( "Carbohydrate (%) 10 12 6
\n" ); document.write( "Iron (%) 5 4 12\r
\n" ); document.write( "\n" ); document.write( " Determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirements of protein; carbohydrates, and iron ( 100% of each). \n" ); document.write( "

Algebra.Com's Answer #826100 by ikleyn(52800) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A dietitian wishes to plan a meal around three foods: The percentages of the daily requirements carbohydrates,
\n" ); document.write( "and iron contained in each ounce of the protein. three foods are summarized in the following table:
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "                     Food I     Food II     Food III\r\n" );
document.write( "Protein (%)           10          6           8\r\n" );
document.write( "Carbohydrate (%)      10         12           6\r\n" );
document.write( "Iron (%)               5          4          12\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Determine how many ounces of each food the dietitian should include in the meal
\n" ); document.write( "to meet exactly the daily requirements of protein; carbohydrates, and iron ( 100% of each).
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "x ounces of Food I;  y ounces of Food II  and  z ounces of Food III.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Write equations as you read the problem\r\n" );
document.write( "\r\n" );
document.write( "    0.10x + 0.06y + 0.08z = 1       (1)    (protein)\r\n" );
document.write( "\r\n" );
document.write( "    0.10x + 0.12y + 0.06z = 1       (2)    (carbohydrates)\r\n" );
document.write( "\r\n" );
document.write( "    0.05x + 0.04y + 0.12z = 1       (3)    (iron)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now you have different options: you can solve the system of equation manually,\r\n" );
document.write( "\r\n" );
document.write( "or use some online solver from the Internet, or use the matrix method of your pocket calculator.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The  ANSWER  is  x = 4, y = 2, z = 6 :  4 ounces of Food I,  2 ounces of Food II,  6 ounces of Food III.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I used online solver www.reshish.com, which is free of charge.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Also, there is similar solver at this site, www.algebra.com.  Its link is \r\n" );
document.write( "\r\n" );
document.write( "https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );