Matrices in the Real World

Example : Coffee Cafe

• 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

5 x+27 y=2.4025x + 7y = 5.60

Example : Coffee Cafe

• Write a linear system to represent the costs.

• Write a matrix equation to represent the linear system.

5 x+27 y=2.4025x + 7y = 5.60

Example : Coffee Cafe

• 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.

BA

Example : Carnival

• 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

x+5 y+z=13.253x + 2y + z = 13.25

Let x be the Scrambler

8x + z = 21.50Let y be the Tilt-a-WhirlLet z be the Bumper Cars

Example : Carnival

• 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.

BA

On your own #1

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.

On your own #1 solution

• 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.

1.5 x+1.5 y=13.022x + y = 13.67

On your own #2

• 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?

On your own #2 solution

• A. Write a system of equations

310x + 5y + 5z = 56.25

Let x be roses

2x + 2y +10z = 34.00

Let y be daisiesLet z be carnations

On your own # 2 solution

• 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.

BA