Secure https/www.mathod 2018 Summer II MATH 1314 002 INT Su Lisa Quntaria 7/24/1

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Secure https/www.mathod 2018 Summer II MATH 1314 002 INT Su Lisa Quntaria 7/24/18 7:39 PM Homework: HW 8.2 Systems of Lin.Eqts:Matrices Score: 0 of 1 p 8.2.79 Tot 9 (6 compiete) ? HW Score: 44 44%, 4 of 9 pts Question Help * A ahou wats a pat tohave a-that has 166 grarms of proten76grams of carbohydates ad 173 5 mngams ottanen A The spa bod service tels the dettan at the dner tor today s salmon slesk, baked eggs and acor squash Each serving of salmon steak has 40 grams of protein 10 grans of atohydralers ad 1 milligram of vitamn A Each serving of baked eggs contains 20 grams of proten, 2 grams of carbohydrates, and 25 miligrams of vitamin A Each provide for the pabentn How many servngs or each tood should the dethan provde? Select conec, choce below and ta ay answer bons 0A The dettan should provde | samen steak (x). baked eggs en and-acorn squash C) you choice Samplity your answers) Them are an efnde hunt er ot combinatons of Servngs ofsamon steak (x). baked eggs on and ocorn soas, cnthal mo dottan can prodeusrg rolets, the solution can be witen a 1o2)xzny real number) Smplity your answers Type expressions using z as the vanable as needed) C. There are no combinations of servings of each food that e dnan can provide Click to select and enter your answeris) and then click Check Answer Check Answer cear All All parts showing

Explanation / Answer

Let the patient have x servings of salmon steak, y servings of baked eggs and z servings of acorn squash. Then, we have 40x+20y+2z = 100…(1), 10x+2y+15z= 70…(2) and x+25y+32z = 173.5…(3).

The augmented matrix of this linear system of equations is A =

40

20

2

100

10

2

15

70

1

25

32

173.5

To solve this linear system of equations, we will reduce A to its RREF as under:

Multiply the 1st row by 1/40

Add -10 times the 1st row to the 2nd row

Add -1 times the 1st row to the 3rd row

Multiply the 2nd row by -1/3

Add -49/2 times the 2nd row to the 3rd row

Multiply the 3rd row by 30/4511

Add 29/6 times the 3rd row to the 2nd row

Add -1/20 times the 3rd row to the 1st row

Add -1/2 times the 2nd row to the 1st row

Then the RREF of A is

1

0

0

5261/4511

0

1

0

20835/9022

0

0

1

16155/4511

Thus, there is a unique solution to the above linear system of equations which is x = 1.2, y = 2.3, and z = 3.6 ( on rounding off to 1 decimal place). Hence the dietician should provide 1 serving of salmon steak, 2 servings of baked eggs and 4 servings of acorn squash (on rounding off to the nearest whole numbers) .

40

20

2

100

10

2

15

70

1

25

32

173.5

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