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(1) One serving of Annie's Organic "Shells and Real Aged Cheddar" Mac and Cheese has270 Calories, 10 g Protein, and 2 g Fiber. Applegate's Organic uncured beef hot dogshave 90 calories per serving with 6 g of protein, and no fiber. A package of Trader Joe'sfrozen Petite Peas has 70 calories per seving with 4 g protein, and 4 g fiber. On lazysummer days, my kids often get some combination of these delights for their lunch whichis why I have all that info at my fingertips.(a) How large of servings of each should be used to meet a 500 Cal, 20 g protein, 5 gfiber meal goal?(b) Look online for the suggested daily doses of Calories, protein, and fiber for a personof your age and gender. Is it possible to get 1/3 of your daily requirements usingthe given ingredients? If not, what is the problem?(c) Find a third ingredient which can be substituted for Hot Dogs to meet 1/3 of yourdaily requirements in Calories, protein, and fiber

Question

This is for a Linear Algebra class. Please provide answer including matrices since this is linear algebra.

(1) One serving of Annie's Organic "Shells and Real Aged Cheddar" Mac and Cheese has
270 Calories, 10 g Protein, and 2 g Fiber. Applegate's Organic uncured beef hot dogs
have 90 calories per serving with 6 g of protein, and no fiber. A package of Trader Joe's
frozen Petite Peas has 70 calories per seving with 4 g protein, and 4 g fiber. On lazy
summer days, my kids often get some combination of these delights for their lunch which
is why I have all that info at my fingertips.
(a) How large of servings of each should be used to meet a 500 Cal, 20 g protein, 5 g
fiber meal goal?
(b) Look online for the suggested daily doses of Calories, protein, and fiber for a person
of your age and gender. Is it possible to get 1/3 of your daily requirements using
the given ingredients? If not, what is the problem?
(c) Find a third ingredient which can be substituted for Hot Dogs to meet 1/3 of your
daily requirements in Calories, protein, and fiber
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(1) One serving of Annie's Organic "Shells and Real Aged Cheddar" Mac and Cheese has 270 Calories, 10 g Protein, and 2 g Fiber. Applegate's Organic uncured beef hot dogs have 90 calories per serving with 6 g of protein, and no fiber. A package of Trader Joe's frozen Petite Peas has 70 calories per seving with 4 g protein, and 4 g fiber. On lazy summer days, my kids often get some combination of these delights for their lunch which is why I have all that info at my fingertips. (a) How large of servings of each should be used to meet a 500 Cal, 20 g protein, 5 g fiber meal goal? (b) Look online for the suggested daily doses of Calories, protein, and fiber for a person of your age and gender. Is it possible to get 1/3 of your daily requirements using the given ingredients? If not, what is the problem? (c) Find a third ingredient which can be substituted for Hot Dogs to meet 1/3 of your daily requirements in Calories, protein, and fiber

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check_circleAnswer
Step 1

Let x represent the intake of Annie's Organic Mac and Cheese , y represent the intake of Applegate's Organic beef hot dog and z represent the serving of Trader Joe's frozen Petite Peas. The corresponding equations become 

Step 2

Solving for x,y,z from these equations, by Cramer's rule :

we obtain x=1.630, y=0.326, z= 0.435

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Step 3

Assumping a daily calories requirement of 1800 cal, protein as 90 g and fiber as 30 g, 1/3rd of this reuirement is 600 cal,30g and 10 g res...

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