Applications of Matrices
Name:
For each problem:
a) Decide which method to use when solving: scalar multiplication, matrix multiplication, or
matrix equations.
b) Set up the problem and SOLVE USING MATRICES!! Show appropriate work.
1.
The drama club sells hot chocolate and hot coffee at the school’s football game to earn money for
a field trip. At one game they sold $200 worth of hot drinks. They used 295 Styrofoam cups that
night. If hot chocolate sells for 75¢ and coffee sells for 50¢, how many of each type of hot drink
did they sell?
scalar multiplication, matrix multiplication, or matrix equations
2. Each year, most people in Virginia have to pay a personal property tax on their vehicles. Assume
each owner has to pay the county 4.5% of the value of their car. Lauren owns a Honda valued at
$28,000. Cliff owns a Ford Explorer valued at $32,550. Jamie’s Hyundai is valued at $8750.
Ray’s Jaguar is valued at $69,330. Show the amount each owner will pay in tax based on the
value of their car.
scalar multiplication, matrix multiplication, or matrix equations
3. Three teams competed in the final round of the Chess Club’s championships. For each win, a team
was awarded three points and for each draw, a team received one point. The blue team had 5 wins
and 4 draws. The red team had 6 wins and 3 draws while the green team had 4 wins ad 5 draws.
Find the total number of points for each team. Which team won the tournament?
scalar multiplication, matrix multiplication, or matrix equations
4. One night Glen Rice of the NBA’s Miami Heat scored a total of 35 points against the Los
Angeles Clippers. In basketball, it is possible to make a 3-point field goal, a 2-point field goal, or
a 1-point free throw. He made as many 2-pointers as 3-pointers and free throws combined. He
scored one point more with 2-pointers than he did with 3-pointers and free throws combined.
How many of each did he make?
scalar multiplication, matrix multiplication, or matrix equations
5. Dave, Sandy, Wally and Kathy are shopping for school supplies. Dave needs 15 computer disks, 6
packages of paper, and 10 pencils. Sandy needs 21 computer disks, 8 packages of paper and 8
pencils. Wally needs 5 computer disks, 15 packages of paper and 25 pencils. Kathy needs 13
computer disks, 10 packs of paper, and 26 pencils. The computer disks cost 75 cents each, $1.19
for a package of paper, and 5¢ for each pencil. Find the total cost per person for their
supplies.
scalar multiplication, matrix multiplication, or matrix equations
6. Dylan, Stephanie, and Kristen go to a Chinese restaurant for lunch and order 3 different lunch
combination platters. Dylan orders 2 portions of fried rice and 1 portion of chicken chow mein.
Stephanie orders 1 portion of fried rice, 1 portion of chicken chow mein, and 1 portion of
sautéed broccoli. Kristen orders 1 portion of sautéed broccoli and 2 portions of chicken chow
mein. Dylan spent$5, Stephanie spent $5.25 and Kristen spent $5.75. How much does 1 portion
of chicken chow mein cost?
scalar multiplication, matrix multiplication, or matrix equations