CP Algebra I
Homework: _______________________________________
6.4 Applications of Linear Systems
Objectives: Solve application problems involving linear systems
You can solve systems of equations by graphing, substitution or elimination. The best method to use
depends on the form of the given equations.
Write a system of equations to model each of the situations on this handout. Then solve the system
using any of the 3 methods we have learned.
I. Model: Finding a Break Even Point
Suppose a club is publishing a newsletter. Expenses are $ .90 for printing and mailing each copy, plus $450
for research and writing. The price of the newsletter is $1.50. per copy. How many newsletters must the
club sell to break even.
Quick Check: Several students decide to start a t-shirt company. After initial expenses of $280, they
purchase each t-shirt wholesale for $3.99. They sell each t-shirt for $10.99. How many must they sell to
break even?
II. Model: Identifying Constraints and Viable Solutions
The local zoo is filling two water tanks for the elephant exhibit. One water tank contains 50 gal of water
and is filled at a constant rate of 10 gal/h. The second water tank contains 29 gal of water and is filled at a
constant rate of 3 gal/h. When will the two tanks have the same amount of water? Explain.
Quick Check: The zoo has two other water tanks that are leaking. One tank contains 10 gal of water and is
leaking at a constant rate of 2 gal/h. The second tank contains 6 gal of water and is leaking at a constant
rate of 4 gal/h. When will the tanks have the same amount of water? Explain.
III. Model: Solving a Wind or Current Problem
Suppose you fly from Miami to San Francisco. It takes 6.5 hours to fly 2600 miles with a head wind. At the
same time, your friend flies from San Francisco to Miami. Her plane travels at the same speed, but her
flight only takes 5.2 hours. Find the average airspeed of the planes. Find the average wind- speed.
(Remember, distance = rate x time)
Quick Check: Suppose you are flying an ultralight aircraft. You fly to a nearby town, 18 miles away. With a
1
3
tail wind, the trip takes hour. Your return flight with a head wind takes hour. Find the average
3
5
airspeed of the ultralight aircraft. Find the average wind- speed.
IV. Model: You have a total of 21 coins, all nickels and dimes. The total value is $1.70. How many nickels
and dimes do you have?
Quick Check: You have a jar of pennies and quarters. You want to choose 15 coins that are worth exactly
$4.35. Set up and solve a system of equations for the situation. Is your answer reasonable in terms of the
original problem?
V. Model: A writing workshop enrolls novelists and poets in a ratio of 5 to 3. There are 24 people at the
workshop. How many novelists are there? How many poets are there?
Quick Check: There are females and males taking a CP Algebra I class. The ratio of girls to boys is 3 to 4.
There are 28 students in the class. How many boys are there? How many girls?
VI. Model: Geometry & Perimeter
The perimeter of a rectangle is 18 inches. The perimeter of a triangle 14 inches. Find the values of x and y.
x
y+1
x
y
y
Quick Check: The perimeter of a rectangle is 36 inches. The perimeter of a triangle 27 inches. Find the
values of n and m.
n+1
m
m
n
n