### Augmented matrices to solve the word problem

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##### Reference no: EM1315859

Question: A firm employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter & 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.

Grams of Nutrients per Tablespoon

 Carbohydrates Protein Peanut Butter 2 6 Oats 5 1

[A] Make an equation for the total amount of carbohydrates.

[B] Make an equation for the total amount of protein.

[C] Solve for the matrix above. Show all work to receive full credit.

[D] How many tablespoons of each will there need to be for the new energy bar?

[E] Determine the augmented matrix that represents the equations from A & B.

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