Question

A dietitian at a hospital wants a patient to have a meal that has 126 grams of protein, 82 grams of carbohydrates, and 101.5 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, 20 grams of
carbohydrates, and 1 milligram of vitamin A Each serving of baked eggs contains 20 grams of protein, 2 grams of carbohydrates, and 25 milligrams of vitamin A Each
serving of acorn squash contains 3 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?
How many servings of each food should the dietitian provide? Select the correct choice below and fill in any answer boxes within your choice.

Answer 1

The dietitian provide 2.5 numbers of salmon steak, 1 baked egg and 2 acorn squash for the patient.

Step-by-step explanation:

Let

Number of salmon steak = x

Number of baked eggs =y

and Number of acorn squash =z

Total amount of protein that is provided to the patient =40 x +20 y+3 z

Total amount of carbohydrates that is provided to the patient = 20 x+2y +15z

Total amount of vitamin A that is provided to the patient = x+25 y+ 37z

According to the problem,

40x+20y+3z=126,     20x+2y+15z=82    and   x+25y+37z= 101.5

Solving the above equations

we get x= 2.5 ,y= 1 and z=2

So ,  The dietitian provide 2.5 numbers of salmon steak, 1 baked egg and 2 acorn squash for the patient.

Answer 2

Following are solution to the given question:

Let x become the number of servings of salmon steak.

Let y represent the number of baked egg slices.

Let z represent the number of acorns squash serves.

Therefore,

Proteins: $40x + 20y + 3z = 126$

Carbohydrates: $20x + 2y + 15z = 82$

Vitamin A: $x + 25y + 37z = 101.5$

So, the equation is:

$\begin{bmatrix} 40 & 20 & 3 \\ 20 &2 & 15 \\ 1 & 25& 37\end{bmatrix} \begin{bmatrix} x\\ y\\ z \end{bmatrix} = \begin{bmatrix} 126\\ 82 \\ 101.5 \end{bmatrix}$

When reducing the matrix to row echelon format, then answers of $x, y, \ and\ z$ are:

$\to x = 2.5\\\\ \to y = 1 \\\\\to z = 2$

Like a result, its solution is as follows: $(x,y,z) = (2.5, 1, 2)$ As a result, the dietitian recommends $2.5$ salmon steaks, $1$ cooked egg, and $2$ acorn squash for the patient.

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