A company’s employees are working to create a new energy

Question

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.

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 above. Show all work to receive full credit

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

carbs protein

Peanut Butter 2 6

Oats 5 1

Answer 1

A (tablespoons of PB) + B (tablespoons of Oats)

Carbs:      A (2) + B (5) = 31

Protein:    A (6) + B (1) = 23, so B = 23 - 6A

Use Carb equation:

2A + 5(23 - 6A) = 31

2A - 30A = 31 - 115

-28A = -84

A = 84/28 = 3 tablespoons of peanut butter

B = 23 - 6(3) = 5 tablespoons of oats