Question

A dietitian at a hospital wants a patient to have a meal that has 113 grams of protein, 54 grams of carbohydrates, and 135.5 milligrams of vitamin A. The hospital foodservice tells the dietitian that the dinner for today is salmon steak, baked eggs, and acorn squash. Each serving of salmon steak has 30 grams of protein, 10 grams ofcarbohydrates, and 1 milligram of vitamin A. Each serving of baked eggs contains 20 grams of protein, 3 grams of carbohydrates, and 20 milligrams of vitamin A. Eachserving of acorn squash contains 4 grams of protein, 15 grams of carbohydrates, and 37 milligrams of vitamin A. How many servings of each food should the dietitian provide for the patient?__ salmon steak (x)__ baked eggs (y)__ acorn squash (z)

Answer 1

Hello there. To solve this question, we'll need to set up a system of equations with 3 equations and 3 variables.

In each equation, we'll have the amounts for protein, carbohydrates and vitamin A.

Talking about protein:

Each serving of salmon steak has 30 grams of protein, baked eggs contains 20 grams of protein and acorn squash contains 4 grams of protein.

Say the servings of salmon steak, baked eggs and acorn squash are the variables x, y and z, respectively. We multiply x, y and z by the respective values for the protein of each serving and add them up. It should be equal to the amount of protein the dietitian was thinking of.

30x + 20y + 4z = 113

Talking about carbohydrates:

The same thing will apply to carbs, we multiply the variables by how many carbs we can get for eachserving. A serving of salmon steak gives you 10 grams of carbs, baked eggs gives you 3 grams of carbs and acorn squash gives you 15 grams.

10x + 3y + 15z = 54

Talking about vitamin A:

Repeat the same process, this time using the values for the vitamin A you get form each serving.

x + 20y + 37z = 135.5

Then we have the following system of equations:

Solving this system of equations, you can use the method of your choice.

After you solved it, you find the values:

1.5 serving of salmon steak, 3 servings of baked eggs and 2 servings of acorn squash.