Question

A nutritionist is performing an experiment on student volunteers. He wishes to feed one of his subjects a daily diet that consists of a combination of three commercial diet foods: Minical contains 50 mg of potassium, 5g of protein and 90 units of vitamin D, Furthermore Liquifast contains 75mg of potassium, 10g of protein and 100 units of potassium, In addition Slimquick containing 10mg of potassium 3g of protein and 50 units of vitamin D. For the experiment it’s important that the subject consume exactly 500 mg of potassium, 75g of protein and 1150 units vitamin D everyday
A1.1 Calculate the system of equation by using Determinant method
A1.2 Analyze the results

Answer 1

Step-by-step explanation:

A nutritionist is performing an experiment on student volunteers. She wants to feed one of the volunteers a daily diet that consists of a combination of three commercial diet foods: MiniCal, LiquiFast, and SlimQuick. For the experiment, it is important that the volunteer consume a total of exactly 500mg of potassium, 75g of protein, and 1150 units of vitamin D every day. The amounts of these nutrients in one ounc every day to satisfy the nutrient requirements exactly? e of each food are given in the table. How many ounces of each food should the volunteer eat MiniCal LiquiFast SlimQuick Potassium (mg) 50 75 Protein (g) Vitamin D (units) 90 10 10 100 50 a) Write a system of equations to model this situation using xy, and z as your variables b) Write the augmented matrix for your system of equations. c) Solve the system algebraically or using the rref in your graphing calculator to find the amount of ounces of each food needed to satisfy the nutrient requirements.

Answer 2

Answer:

The daily consumption includes 47.8mg of potassium, 101g of protein, and 26.5 units of vitamin D.

Step-by-step explanation:

Let the x be the quantity of Minical consumed, y be the quantity of Liquifast consumed, and z be the quantity of Slimquick consumed..

The consumption should be 500mg of potassium, 75g of protein, and 1150 units of vitamin D.

Therefore, the equations are

50x + 75y + 10z = 500 ...(i)

5x + 10y + 3z = 75 ...(ii)

90x + 100y + 50z = 1150 ...(iii)

Representing the above equations in determinant form, we get

$D=\left[\begin{array}{ccc}50&5&90\\75&10&100\\10&3&50\end{array}\right]$

D = 50(500-300) - 5(3750-1000) + 90(225-100)

D = 50(200) - 5(2750) + 90(125)

D = 7500

Replacing the x coefficients with the constants.

$D_x = \left[\begin{array}{ccc}500&5&90\\75&10&100\\1150&3&50\end{array}\right]$

$D_x$ = 500(500-300) - 5(3750-115000) + 90(225-11500)

$D_x$ = 500(200) - 5(-111250) + 90(-11275)

$D_x$ = 358500

Replacing the y coefficients with the constants.

$D_y=\left[\begin{array}{ccc}50&500&90\\75&75&100\\10&1150&50\end{array}\right]$

$D_y$ = 50(3750-115000) - 500(3750-1000) + 90(86250-750)

$D_y$ = 50(-111250) - 500(2750) + 90(85500)

$D_y$ = 757500

Replacing the z coefficients with the constants.

$D_z=\left[\begin{array}{ccc}50&5&500\\75&10&75\\10&3&1150\end{array}\right]$

$D_z$ = 50(11500-225) - 5(86250-750) + 500(225-100)

$D_z$ = 50(11275) - 5(85500) + 500(125)

$D_z$ = 198750

Now, $x = \frac{D_x}{D}$, $y = \frac{D_y}{D}$, and $z = \frac{D_z}{D}$

$x = \frac{358500}{7500}$

x = 47.8

$y = \frac{757500}{7500}$

y = 101

$z = \frac{198750}{7500}$

z = 26.5

Therefore, the daily consumption must include 47.8mg of potassium, 101g of protein, and 26.5 units of vitamin D.

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