Explanation Given: A doctor recommends that a patient take 50 mg each of niacin, riboflavin, and thiamin daily to alleviate a vitamin deficiency. In his medicine chest at home, the patient finds three brands of vitamin pills. The following table gives the amounts of the relevant vitamins per pill: VitaMax Vitron VitaPlus Niacin (mg) 5 10 15 Riboflavin (mg) 15 20 0 Thiamin (mg) 10 10 10 Table ( 1 ) Approach: Let x , y , and z represents the number of pills in VitaMax, Vitron, and VitaPlus respectively, to get 50 mg of each vitamin. Write the augmented matrix of the system. Use elementary row operations to change the augmented matrix to row-echelon form. Write the new system of equations that corresponds to the row-echelon form of the augmented matrix and solve by back-substitution. Calculation: Since the vitamins required is 50 mg. The system of equations is given below. 5 x + 10 y + 15 z = 50 15 x + 20 y = 50 10 x + 10 y + 10 z = 50 Consider the system of equations { 5 x + 10 y + 15 z = 50 15 x + 20 y = 50 10 x + 10 y + 10 z = 50 . The augmented matrix is given by, [ 5 10 15 50 15 20 0 50 10 10 10 50 ] Transform the augmented matrix into row echelon form. Perform the transformation R 1 → R 1 5 . [ 5 5 10 5 15 5 50 5 15 20 0 50 10 10 10 50 ] → [ 1 2 3 10 15 20 0 50 10 10 10 50 ] Perform the transformation R 2 → R 2 − 15 R 1 . [ 1 2 3 10 15 − 15 ( 1 ) 20 − 15 ( 2 ) 0 − 15 ( 3 ) 50 − 15 ( 10 ) 10 10 10 50 ] → [ 1 2 3 10 0 − 10 − 45 − 100 10 10 10 50 ] Perform the transformation R 3 → R 3 − 10 R 1 . [ 1 2 3 10 0 − 10 − 45 − 100 10 − 10 ( 1 ) 10 − 10 ( 2 ) 10 − 10 ( 3 ) 50 − 10 ( 10 ) ] → [ 1 2 3 10 0 − 10 − 45 − 100 0 − 10 − 20 − 50 ] Perform the transformation R 2 → − R 2 10

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 11.1, Problem 69E

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The number of pills required to get 50 mg of each vitamin.

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Chapter 11.1, Problem 68E

Chapter 11.1, Problem 70E

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Chapter 11 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 11.1 - If a system of linear equations has infinitely...Ch. 11.1 - Write the augmented matrix of the following system...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - 5-10 Dimension of a Matrix State the dimension of...Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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The number of pills required to get 50 mg of each vitamin.

Solution Summary: The author explains that a doctor recommends taking 50 mg of niacin, riboflavin, and thiamin daily to alleviate vitamin deficiency.

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To find: The number of pills required to get 50 mg of each vitamin.

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Chapter 11 Solutions

To find:

The number of pills required to get 50 mg of each vitamin.