Could you please explain me this question/solution step by step? A dietitian wishes to plan a meal around three foods. The meal is to include 6,800 units of vitamin A, 2,590 units of vitamin C, and 810 units of calcium. The number of units of the vitamins and calcium in each ounce of the foods is summarized in the following table.Food I Food II Food IIIVitamin A 400 1200 800Vitamin C 110 570 340 Calcium 90 30 60 Determine the amount of each food the dietitian should include in the meal in order to meet the vitamin and calcium requirements. (Let x, y, and z denote the number of ounces of Food I, Food II, and Food III, respectively.
We are asked to find the amount of three different foodstuffs to prepare in order to meet the requirements of particular vitamins/minerals. The amount of each for each foodstuff is given below:
`([Food I,Food II, Food III, Total],[400,1200,800,6800],[110,570,340,2590],[90,30,60,810])`
We can set up a system of linear equations. As suggested, let x be the number of ounces of Food I, y the oz of Food II, and z the oz of Food III.
The amount of vitamin A we get from Food I is 400x. (For each ounce of I we get 400 units of vitamin A.) Likewise the amount from II is 1200y and the amount from III is 800z. The total is the sum from each food type and must equal 6800 so:
In a similar fashion we find that for...
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