7.4 NOTES Applying Linear Systems
There are many situations when you would use a system of equations to solve a real-world
problem. Here are a few examples:
1. Suppose your community center sells a total of 292 tickets for a basketball game. An adult
ticket costs $3. A student ticket costs $1. The sponsors collect $470 in ticket sales. Write and
solve a system to find the number of each type of ticket sold.
Define the variable(s): What are we trying to solve for? (Usually the last sentence)
Relate the problem: What are the two totals we are working with?
Write two equations: (How would I find each total?)
Now you can use any method to solve this system (graphing, substitution, elimination). What
method do you think would be the best?
2. Suppose a model airplane club publishes a newsletter. Expenses are $.9 for printing and
mailing each copy, plus $600 total for research and writing. The price of a newsletter is $1.50
per copy. How many copies of the newsletter must the club sell to break even?
Define the variable(s): What are we trying to solve for? (Usually the last sentence)
Relate the problem: What are the two totals we are working with?
Write two equations: (How would I find each total?)
Now you can use any method to solve this system (graphing, substitution, elimination). What
method do you think would be the best?
PRACTICE:
3. Suppose an antique car club publishes a newsletter. Expenses are $.35 for printing and
mailing each copy, plus $770 total for research and writing. The price of the newsletter is $.55
per copy. How many copies of the newsletters must the club sell to break even?
4. Tyrel and Dalia both some pens and pencils. Tyrel bought 4 pens and 5 pencils, which cost
him $6.71. Dalia bought 5 pens and 3 pencils, which cost her $7.12. Let a equal the price of a
pen. Let b equal the price of a pencil.
a. Write an equation that relates the number of pens and pencils Tyrel bought to the
amount he paid for them.
b. Write an equation that relates the number of pens and pencils Dalia bought to the
amount she paid for them.
c. Solve the system you wrote for parts (a) and (b) to find the price of a pen and the price
of a pencil.
5. Your class sells a total of 64 tickets to a play. A student ticket costs $1, and an adult ticket
costs $2.50. You class collects $109 in total ticket sales. How many adult tickets did you sell?
How many student tickets did you sell?
6. Your teacher is giving you a test worth 100 points containing 40 questions. There are two-point
and four-point questions on the test. How many of each type of question are on the test?