Solve Lin. System of Eqns w/ Matrices: ingredients

[kimperryman]

3. 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 22 carbohydrates and 14 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.

      Carbs Protein
P. B.   2     4
Oats    8     1

A. Write an equation for the total amount of carbohydrates.

B. Write an equation for the total amount of protein.

C. Determine the augmented matrix that represents the previous two equations.

D. Solve for the previous matrix. Show all work to receive full credit.

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

 

[stapel]

3. 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 22 carbohydrates and 14 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.

      Carbs Protein
P. B.   2     4
Oats    8     1

What variables did you pick? How did you define them? What equations have you developed? What matrix did you get? Where are you stuck?

Please be complete. Thank you!

Eliz.

 

[kimperryman]

I think i figured out what to do with the equations but I am having a hard time pulling the equations out of the word problems. Can someone help me with this and I think i can do the rest once i have that????

 

[stapel]

The set-up just uses the same "translation" skills you've been using all along: Start at the beginning. What are you asked to find? (Hint: Ingredients.) What variables did you pick to represent these unknown amounts? (Hint: "P" for "peanut butter" and "G" for "grain" -- since "O" for "oats" would be too easy to mis-read -- might be good choices.)

Once you have variables for the unknown amounts, look at the definitions in the exercise. What expression would represent the amount of carbs from a given (but currently unknown) amount of the ingredients? (Hint: You'll be using the variables, and adding.) Do the same sort of thing for the amount of protein from these ingredients.

Then look at the limits. What equations can be formed from the expressions for carbs and proteins? (Hint: Set the expressions equal to the given desired amounts.)

If you get stuck, please reply showing how far you have gotten. Thank you!

Eliz.