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Question 142041: I am quite confused when it comes to the augmented matrix. I have been working on this problm for four hours and have gotten even more confused. Any assistance with this problem would be greatly appreciated.
A company’s employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 31 carbohydrates and 23 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices. I need to process the following by utilizing the table below. I need to write an equation for the total amount of carbohydrates. Write an equation for the total amount of protein.Determine the augmented matrix that represents the equations from A and B. Solve for the matrix and determine how many tablespoons of each will there need to be for the new energy bar?
Grams of Nutrients per tablespoon
Peanut Butter with 2 grams of Carbohydrates and 6 grams of protein
Oats with 5 grams of Carbohydrates and 1 grams of protein
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A company’s employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete.
They want a total of 31 carbohydrates and 23 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices. I need to process the following by utilizing the table below. I need to write an equation for the total amount of carbohydrates. Write an equation for the total amount of protein.Determine the augmented matrix that represents the equations from A and B. Solve for the matrix and determine how many tablespoons of each will there need to be for the new energy bar?
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They want a total of 31 carbohydrates and 23 grams of protein to make the bar sufficient.
Let "p" be number of tablespoons of peanut butter
Let "t" be number of tablespoons of Oats
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Grams of Nutrients per tablespoon
Peanut Butter with 2 grams of Carbohydrates and 6 grams of protein
Oats with 5 grams of Carbohydrates and 1 grams of protein
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EQUATIONS:
Carbo Equation: 2p + 5t = 31
Protein Eq : 6p + t = 23
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Use any method to solve to get:
p = 3 (# of tablespoons of peanut butter)
t = 5 (# of tablespoons of Oats)
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Cheers,
Stan H.
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