To determine To calculate: Amount of grams of each mix should be used to obtain the right diet provided that Bill’s dog is on a strict diet and is to receive 20 grams of protein and 6 grams of carbohydrates and he has only two food mixes available, Mix A having 10 % protein and 6 % carbohydrates and Mix B having 20 % protein and 2 % carbohydrates. Explanation Given Information: Bill’s dog is on a strict diet and is to receive 20 grams of protein and 6 grams of carbohydrates and he has only two food mixes available, Mix A having 10 % protein and 6 % carbohydrates and Mix B having 20 % protein and 2 % carbohydrates. Formula used: Addition or Elimination method to solve a linear system of equations: Step1. Write the equations in the form of a x + b y = c . Step2. Multiply one or both equations by a constant, so that after adding the equations, there will be only one variable. Step3. Add both the equations which will result in equation of one variable. Step4. Compute the equation obtained in step3 and find the value of one variable. Step5. Put the value obtained in step4 of one variable in any of the original equation to obtain other one. Step6. Write the value of variables in correct order. Step7. Check the solution by putting the calculated value in all equations in the system. Calculation: Suppose the amount of Mix A used is x and the amount of Mix B used is y. Bill used x amount of Mix A having 10 % protein with y amount of Mix B having 20 % protein to obtain 20 grams of protein, the first equation is, 0.10 x + 0.20 y = 20 Bill used x amount of Mix A having 6 % carbohydrates with y amount of Mix B having 2 % carbohydrates to obtain 6 grams of carbohydrates, the second equation is, 0.06 x + 0.02 y = 6 The system of two equations is: 0.10 x + 0.20 y = 20 …… ( 1 ) 0.06 x + 0.02 y = 6 …… ( 2 ) Use equation ( 1 ) and equation ( 2 ) to eliminate x and solve for y : Multiply equation ( 2 ) by − 10 , 0.10 x + 0.20 y = 20 − 0.60 x − 0.20 y = − 60 _ − 0.50 x = − 40 Solve further as, − 0

Intermediate Algebra For College Students (10th Edition)

10th Edition

ISBN: 9780134758992

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 4.3, Problem 35ES

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To calculate: Amount of grams of each mix should be used to obtain the right diet provided that Bill’s dog is on a strict diet and is to receive 20 grams of protein and 6 grams of carbohydrates and he has only two food mixes available, Mix A having 10% protein and 6% carbohydrates and Mix B having 20% protein and 2% carbohydrates.

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Chapter 4.3, Problem 34ES

Chapter 4.3, Problem 36ES

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