Matrices and Systems of Equations

1. To raise money, the local baseball teams decided to sell team logo hats (H) and T-shirts (T). The league director decided to hold a contest among the teams to see which team can raise the most money. The contest lasted for 3 weeks. Here are the results of the first 2 weeks. The numbers represent the number of hats and T-shirts sold.

A. How much of each item had the teams sold by the end of the second week. Use matrices to solve the problem. Final answer must be given in matrix form. Show all work to receive full credit.

B. Which team had sold the most items at the end of the second week, and how many total items did they sell?

C. By the end of the third week, the totals were as follows:

D. Which baseball team won the contest, and what was their total sales?

2. Use augmented matrices to solve the following systems of equations. Show all work to receive full credit. Final answer must be given in matrix form.

A.

Answer:

B.

Answer:

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.

Carbohydrates Protein
Peanut Butter 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?

4. A total of 700 tickets were sold for a musical. Senior citizen tickets sold for $15, children tickets sold for $20, and adult tickets sold for $25; the total earnings from ticket sales was $15,750. Five times more children tickets were sold than senior citizen tickets. How many tickets of each type were sold? Set up a system of three equations and three unknowns, use an augmented matrix to solve, and show all work to receive full credit.

A. What are the three unknowns?

B. Write a separate equation representing each of the first three sentences of the word problem.

C. Determine the augmented matrix that represents the three equations.

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

E. How many of each type of ticket were sold?
MTH 212