Matrices in the Real World

1. Matrices in the Real World

2. Remember… Steps to creating an equation from context • Read the problem statement • Identify the known quantities • Identify the unknown variables • Create an equation using the known quantities and the variables you found. Keep in mind… • In systems of equations, you will have 2 or 3 equations (hence the “system” part). Therefore, you will have to decide which quantities and variables belong together.

3. Cam’s Coffee Café serves coffee with different amounts of caffeine, which is sold in 32 ounce cups. The Good Morning blend combines 25 ounces of caffeinated coffee with 7 ounces of decaf, and sells for $5.60. The Nighty Night blend combines 5 ounces of caffeinated coffee with 27 ounces of decaf and sells for $2.40. What is the customer cost for one ounce of caffeinated coffee and one ounce of decaf? Let x be caffeinated coffee, and y be decaf. • Write a linear system to represent the costs 25x + 7y = 5.60 Example : Coffee Cafe

4. Write a linear system to represent the costs. • Write a matrix equation to represent the linear system. 25x + 7y = 5.60 Example : Coffee Cafe

5. Write a matrix equation to represent the linear system. • Find the cost per ounce for caffeinated and decaf. So, caffeinated coffee costs $0.21 per ounce and decaf costs $0.05 per ounce. A B Example : Coffee Cafe

6. Mama’s Country Catering serves the best meatloaf in town. Mama uses a blend of ground beef and ground pork to make two different versions of her famous 3 pound meatloaf. For the Beefeater, Mama combines 2 pounds of ground beef with 1 pound of ground pork and sells for $13.67. The Porker combines 1.5 pounds of ground beef with 1.5 pounds of ground pork and sells for $13.02. • A. Write a linear system to represent the costs. • Let x be ground beef, and y be ground pork. • B. Write a matrix equation to represent the linear system. • C. Find the cost per pound for ground beef and ground pork. Example: Country Catering

7. A. Write a linear system to represent the costs. • B. Write a matrix equation to represent the linear system. • C. The ground beef is $4.99 per pound, the ground pork is $3.69 per pound. 2x + y = 13.67 Example: Country Catering

8. The annual carnival opened at Arbor Place Mall. Jamal attended the carnival the first three nights that it was open. On Monday, Jamal spent $13.25 and rode The Scrambler 3 times, the Tilt-a-Whirl twice and the Bumper Cars one time. He spent the same amount on Tuesday, riding The Scrambler and the Bumper Cars one time each, and the Tilt-a-Whirl 5 times. On Wednesday, Jamal rode the Bumper Cars once but when he felt sick after riding The Scrambler 8 times in a row he went home. He spent $21.50 for his night of fun on Wednesday. • Write a system of equations 3x + 2y + z = 13.25 Let x be the Scrambler Example : Carnival Let y be the Tilt-a-Whirl 8x + z = 21.50 Let z be the Bumper Cars

9. Set up a matrix equation to represent the system. • Find the cost per activity. So, The Scrambler cost $2.25, the Tilt-a-Whirl cost $1.50 and the Bumper Cars cost $3.50. B A Example : Carnival

10. Buckets of Blossoms uses roses, daisies, and carnations to make three of their beautiful bouquets. The most expensive bouquet, Rosie, sells for $56.25 and includes 10 roses, 5 daisies and 5 carnations. Daisy-head includes 3 roses, 10 daisies and 3 carnations, and sells for $41.50. The least expensive bouquet sells for $34.00, and includes 2 roses, 2 daisies and 10 carnations. • A. Write a system of equations. • B. How much does each type of flower cost? Example: Buckets of Blossoms

11. A. Write a system of equations Let x be roses Let y be daisies Let z be carnations 10x + 5y + 5z = 56.25 3 2x + 2y +10z = 34.00 Example: Buckets of Blossoms

12. Set up a matrix equation to represent the system. • Find the cost per type of flower. B. So, a rose costs $3.25, a daisy costs $2.50 and a carnation costs $2.25. B A Example: Buckets of Blossoms

13. On Your Own #1 The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5,050 is collected. How many children and how many adults attended?

14. On Your Own #2 Two small pitchers and one large pitcher can hold 8 cups of water.  One large pitcher minus one small pitcher constitutes 2 cups of water.  How many cups of  water can each pitcher hold?

15. On Your Own #3 A test has twenty questions worth 100 points.  The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each.  How many multiple choice questions are on the test?