SOLUTION: 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 summ

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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:
Food I Food II Food III
Protein (%) 10 6 8
Carbohydrate (%) 10 12 6
Iron (%) 5 4 12
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).
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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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:

                     Food I     Food II     Food III
Protein (%)           10          6           8
Carbohydrate (%)      10         12           6
Iron (%)               5          4          12

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).
~~~~~~~~~~~~~~~~~~~~ 


x ounces of Food I;  y ounces of Food II  and  z ounces of Food III.


Write equations as you read the problem

    0.10x + 0.06y + 0.08z = 1       (1)    (protein)

    0.10x + 0.12y + 0.06z = 1       (2)    (carbohydrates)

    0.05x + 0.04y + 0.12z = 1       (3)    (iron)


Now you have different options: you can solve the system of equation manually,

or use some online solver from the Internet, or use the matrix method of your pocket calculator.


The  ANSWER  is  x = 4, y = 2, z = 6 :  4 ounces of Food I,  2 ounces of Food II,  6 ounces of Food III.


I used online solver www.reshish.com, which is free of charge.


Also, there is similar solver at this site, www.algebra.com.  Its link is 

https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver

Solved.