A dietitian wishes a patient to have a meal that has 41 gram

A dietitian wishes a patient to have a meal that has 41 grams of protein, 64.5 grams of carbohydrates, and 660 milligrams of calcium. The hospital food service tells the dietitian that the dinner for today is chicken, corn, and milk. Each serving of chicken has 40 grams of protein, 45 grams of carbohydrates, and 100 milligrams of calcium. Each serving of corn has 3 grams of protein, 16 grams of carbohydrates, and 10 milligrams of calcium. Each glass of milk has 9 grams of protein, 13 grams of carbohydrates, and 300 milligrams of calcium. How many servings of each food should the dietitian provide for the patient? Select the correct choice below and fill in any answer boxes in your choice. A. The patient should have serving(s) of chicken, serving(s) of corn, and serving(s) of milk. (Simplify your answers.) B. There are infinitely many solutions. C. There is no solution.

Solution

Letx servings of chicken

y servings of corn

z servings of milk

Now Total protein in all three : 40x +3y +9z = 41

Now Total carbs in all three: 45x +16y +13z = 64.5

Now Total calcium in all three : 100x +10y + 300z = 660

Now solve all the three equations to get x, y , z :

x = 1/2 , y =1 ; z= 2

Patient should have half sering of chicken , 1 serving of corn and 2 servings of milk