Explanation Given: Rabbits are to be given daily diet that includes 30 grams of protein, 16 grams of fat, and 24 grams of carbohydrates. The three food mixes that are available with the grams of nutrient per unit are given below. Protein Fat Carbohydrate Mix A 4 6 3 Mix B 6 1 2 Mix C 4 1 12 Calculation: 1. Understand: Assume x to be the quantity of Mix A, y to be the quantity of Mix B and z to be quantity of Mix C. 2. Translate: Translate the given conditions into an equation. 30 grams of protein is needed every day. Use table to combine the protein units of all three mixes A, B, and C. Translate this into an equation of the form 4 x + 6 y + 4 z = 30 . 16 grams of fat is needed every day. Use table to combine the fat units of all three mixes A, B, and C. Translate this into an equation of the form 6 x + y + z = 16 . 24 grams of carbohydrate is needed every day. Use table to combine the carbohydrate mixes of three units A, B, and C. Translate this into an equation of the form 3 x + 2 y + 12 z = 24 . 3. Solve: The first equation is, 4 x + 6 y + 4 z = 30 …… (1) The second equation is, 6 x + y + z = 16 …… (2) The third equation is, 3 x + 2 y + 12 z = 24 …… (3) Multiply the equation (2) by − 2 . − 2 ( 6 x + y + z ) = − 2 ( 16 ) − 12 x − 2 y − 2 z = − 32 …… (4) Add equation (4) to equation (3) to eliminate y . 3 x + 2 y + 12 z = 24 − 12 x − 2 y − 2 z = − 32 _ − 9 x + 10 z = − 8 …… (5) Multiply the equation (2) by − 6 . − 6 ( 6 x + y + z ) = − 6 ( 16 ) − 36 x − 6 y − 6 z = − 96 …… (6) Add equation (6) to equation (1) to eliminate y . 4 x + 6 y + 4 z = 30 − 36 x − 6 y − 6 z = − 96 _ − 32 x − 2 z = − 66 …… (7) Multiply equation (7) by 5. 5 ( − 32 x − 2 z ) = 5 ( − 66 ) − 160 x − 10 z = − 330 …… (8) Add equation (8) to equation (5) to find the value of x

7th Edition

ISBN: 9780135923290

Author: Martin-Gay

Publisher: PEARSON

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Question

Chapter 4.3, Problem 37E

To determine

The units of each mix that are needed to meet the daily dietary needs.

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Chapter 4.3, Problem 36E

Chapter 4.3, Problem 38E

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Chapter 4 Solutions

EFSC MML FOR MAT 1033

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

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