Modeled the word problem mathematically like system of equations and solve by the matrix method.
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. Show all work to receive full credit.
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Grams of Nutrients per Tablespoon
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Carbohydrates
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Protein
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Peanut Butter
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2
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6
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Oats
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5
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1
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Write an equation for the total amount of carbohydrates.