A dietitian at a hospital wants a patient to have a meal that has 109 grams of protein, 76

grams of carbohydrates, and 93.5 milligrams of vitamin A The hospital food service tells

the dietitian that the dinner for today is salmon steak, baked eggs, and acorn squash.

Each serving of salmon steak has 40 grams of protein, 30 grams of carbohydrates, and 1

milligram of vitamin A. Each serving of baked eggs contains 15 grams of protein, 2 grams

of carbohydrates, and 20 milligrams of vitamin A. Each serving of acorn squash contains

4 grams of protein, 25 grams of carbohydrates, and 32 milligrams of vitamin A. How many

servings of each food should the dietitian provide for the patient?

Question

Mathematics

Answered

A dietitian at a hospital wants a patient to have a meal that has 109 grams of protein, 76

grams of carbohydrates, and 93.5 milligrams of vitamin A The hospital food service tells

the dietitian that the dinner for today is salmon steak, baked eggs, and acorn squash.

Each serving of salmon steak has 40 grams of protein, 30 grams of carbohydrates, and 1

milligram of vitamin A. Each serving of baked eggs contains 15 grams of protein, 2 grams

of carbohydrates, and 20 milligrams of vitamin A. Each serving of acorn squash contains

4 grams of protein, 25 grams of carbohydrates, and 32 milligrams of vitamin A. How many

servings of each food should the dietitian provide for the patient?

Answer :

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Oeerivonago Oeerivonago · Answer 1

The number of variables and the number of unknowns are equal, therefore, the system can be solved by simultaneous equation

The required number of servings are;

Number of servings of salmon steak is 1.5 servings

Number of servings of baked eggs is 3 servings

Number of servings of acorn squash is 1 serving

Reason:

Given parameter;

Required mass of protein = 109 gram

Required mass of carbohydrate = 76 grams

Required mass of vitamins = 93.5 mg

The dinner = Salmon steak, baked eggs, and acorn squash

Mass of protein in a salmon steak serving = 40 grams

Nutrition value of salmon steak;

Protein = 40 grams

Carbohydrate = 30 grams

Vitamin A. = 1 milligram

Nutrition value of baked eggs;

Protein = 15 grams

Carbohydrate = 2 grams

Vitamin A. = 20 milligrams

Nutrition value of acorn squash;

Protein = 4 grams

Carbohydrate = 25 grams

Vitamin A. = 32 milligrams

Let A represent the amount of serving of salmon steak, let B represent the

number of serving of baked eggs, and let C represent the number of

servings of acorn squash, we have;

40·A + 15·B + 4·C = 109

30·A + 2·B + 25·C = 76

A + 20·B + 32·C = 93.5

Solving the above simultaneous equation with a graphing calculator gives;

A = 1.5, B = 3, C = 1

Therefore, the dietician should provide 1.5 serving of salmon stake, 3

servings of baked eggs, and 1 serving of acorn squash

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