Setting up and solving a system of Equations
1. While on a stakeout protecting Earth from the scum of the universe, Agent
Cooper observed five men in black enter a coffee shop and get three
doughnuts and five coffees for $3.30. Next, three aliens in disguise entered
the shop and got four doughnuts and three coffees for $2.75.
a. Define the variables you will use to model the situation.
b. Write the system of equations that describes the situation.
c. Solve the system algebraically to find the cost per doughnut and the cost
per cup of coffee.
d. Agent Cooper saw Agent Wilson enter the same shop; she got two
doughnuts and two cups of coffee. How much was Agent Wilson’s bill?
2. Tables and Chairs. A man and his daughter manufacture unfinished tables
and chairs. Each table requires 3 hours of sawing and 1 hour of assembly.
Each chair requires 2 hours of sawing and 2 hours of assembly. Together,
the two of them do 12 hours of sawing and 8 hours of assembly work each
day. Find a system of equations that describes the number of tables and
chairs they can make daily.
a. Define the variables.
b. Determine the resources available for manufacturing the tables and
chairs.
c. Write the system of equations to describe the relationship between each
resource and the variables.
d. Solve the system.
3. Chicken Farm. Amy’s Chicken Farm is a producer of frying chickens. In
order to produce the best fryers possible, the regular chicken feed is
supplemented by two vitamins. The amount of each vitamin required per 100
ounces of feed is: Vitamin B, 50 units and Vitamin C, 60 units. Two
supplements are available to add to the feed. Supplement I contains 5 units of
Vitamin B per ounce and 10 units of Vitamin C per ounce. Supplement II
contains 25 units of Vitamin B per ounce and 10 units of Vitamin C per ounce.
How much of each supplement should Danny buy to add to each 100 ounces
of feed?
Setting up and solving a system of Equations
HOMEWORK:
1. The Wellborn Corporation offers two different stocks options for investors.
One share of Premium stock costs $10.55 and has a history of increasing
$0.25 per week. The corporation also offers shares of Gold stock for
$18.05 per share and has a history of increasing by $0.15 per week. You
plan to purchase one of each stock.
a. Assuming each stock continues to perform as it has historically, find
the equation for the price of each stock. Use t to represent the
number of weeks you own the stock. Let P(t) represent the value
(in dollars) of your Premium stock and let G(t) represent the value
(in dollars) of your Gold stock.
b. After how many weeks will the price of your two stocks be the
same? At what price does this occur?
c. During what time period is the Premium stock worth more than the
Gold stock?
2. Shawls and Afghans. Carmella and Walt produce handmade shawls
and afghans. They spin the yarn and then weave it. A shawl requires 1
hour of spinning and 1 hour of weaving. An afghan needs 2 hours of
spinning and 4 hours of weaving. Together, they spend 8 hours of
spinning and 14 hours of weaving. How many of each item can they
make?
a. Define the variables.
b. Write an equation for the two parts of the production process.
c. Solve the system.
3. Appliance Repair Shop. An appliance repair shop has 5 vacuum
cleaners and 18 DVD players to be repaired. The store employs two parttime repair people. Kathy can repair 1 vacuum cleaner and 3 DVD players
per week, while Sandy can repair 1 vacuum cleaner and 6 DVD players
per week. How many weeks do they have to work together to complete all
the repairs?