Matrices in the Real World
Matrices in the Real World. Example 1: Computer Costs Computer Warehouse sells netbook computers for $350, desktops for $500 and laptops for $850. Their.
Jan 18, 2018
Example 1: Computer Costs Computer Warehouse sells netbook computers for $350, desktops for $500 and laptops for $850. Their competitor, Computers R Us, sells netbook computers for $300, desktops for $600 and laptops for $775. B. Create and label a matrix that represents the prices for Computers R Us. NetbooksDesktops Laptops
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Matrices in the Real World
Example 1: Computer Costs
β’ Computer Warehouse sells netbook computers for $350, desktops for $500 and laptops for $850. Their competitor, Computers R Us, sells netbook computers for $300, desktops for $600 and laptops for $775.
A. Create and label a matrix that represents the prices for Computer Warehouse.
πΆππππ’π‘ππ hππππ ππ’π πππππππ =[ 3 50 500 850 ]Netbooks Desktops Laptops
Example 1: Computer Costs
β’ Computer Warehouse sells netbook computers for $350, desktops for $500 and laptops for $850. Their competitor, Computers R Us, sells netbook computers for $300, desktops for $600 and laptops for $775.
B. Create and label a matrix that represents the prices for Computers R Us.
πΆππππ’π‘πππ π ππ ππππππ = [3 00 600 775 ]Netbooks Desktops Laptops
Example 1: Computer Costs
β’ Computer Warehouse sells netbook computers for $350, desktops for $500 and laptops for $850. Their competitor, Computers R Us, sells netbook computers for $300, desktops for $600 and laptops for $775.
C. Subtract the matrices to find the difference between the prices of the two stores.
[ 350 500 850 ]β [ 3 00 600 775 ]=ΒΏNetbooks Desktops Laptops
[ 5 0 β100 75 ]
Example 2: Coffee Cafe
β’ Camβs Coffee CafΓ© 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.β’ Write a linear system to represent the costs
5 x+27 y=2.4025x + 7y = 5.60
Example 2: Coffee Cafe
β’ Write a linear system to represent the costs.
β’ Write a matrix equation to represent the linear system.
5 x+27 y=2.4025x + 7y = 5.60
Example 2: Coffee Cafe
β’ Write a matrix equation to represent the linear system.
β’ 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 3: Carnival
β’ 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.
β’ 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 3: Carnival
β’ Set up a matrix equation to represent the system.
β’ 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
β’ The football concession stand sells hotdogs for $3.50, pretzels for $2.50 and nachos for $3.00. The booster club buys hotdogs for $3.25, pretzels for $1.50 and nachos for $1.75 to sell in the concession stand.
A. Create and label a matrix that represents the customer prices for each of the items.B. Create and label a matrix that represents the prices that the booster club buys the items for.C. Subtract the matrices to determine the amount of profit the booster club makes on each item.
On your own #1 solution
A.
B.
C.
cuhotdogs pretzels nachos
Booster clubhotdogs pretzels nachos
[ 3 .50 2.50 3.00 ]β [ 3 .25 1.50 1.75 ]=ΒΏ
[ .25 1.00 1.25 ]hotdogs pretzels nachos
On your own #2
Mamaβs 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. β’ A. Write a linear system to represent the costs.β’ Let x be ground beef, and y be ground pork.
β’ B. Write a matrix equation to represent the linear system.β’ C. Find the cost per pound for ground beef and ground pork.
On your own #2 solution
β’ A. Write a linear system to represent the costs.
β’ B. Write a matrix equation to represent the linear system.
β’ 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 you own #3
β’ 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.
β’ A. Write a system of equations.β’ B. How much does each type of flower cost?
On you own #3 solution
β’ 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 # 3 solution
β’ Set up a matrix equation to represent the system.
β’ 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
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