PS9 - Unit 4 Summative Prep – Part 2
Standard 1: Concepts and Procedures
4.1: Solving Graphically
Solve each system of equations graphically. Clearly record and describe the solution
(consistent independent, consistent dependent, inconsistent).
1.
2.
3. Describe the three types of solutions and what you may recognize graphically and within an equation
to identify them.
4.2: Solving with Substitution and 4.3: Solving with Elimination
4.
Solve using substitution.
5.
Solve using either substitution or elimination.
6.
7.
8.
9.
4.4: Solving Systems of Inequalities
Solve each system of inequalities graphically.
10.
11.
12.
13.
Solve using elimination.
Standard 2: Problem Solving
Solve each context problem by solving a system of equations or inequalities. If you use your GDC to
solve, write “GDC” and record your answer. Otherwise, show your work algebraically.
1.
Lego Land has an entrance fee of $10 while the cost per ride is $1. Water World has an entrance
fee of $7 but the cost per ride is $2. (Thanks for the question, Claire C.!)
a.
b.
c.
2.
Ms. Smith has two tutoring lesson plans. The Regular Class Plan charges $22.50 for every tutoring
session. The Math Gifted Class Plan has a $17.50 membership fee and charges $19 for each
tutoring class. (Thanks for the question, Clayton!)
a.
b.
c.
d.
3.
c.
d.
Create a system of equations to represent the scenario.
How many pizzas bought would give the same price for each pizzeria? How much would it
cost?
If Bob wanted to buy 5 pizzas, who would be the better choice?
If Bob has $40, which pizzeria would buy him more pizza?
Mike’s bikes charges $4 for each 30 minutes you bike and a fixed cost of $5.50. Sally’s rental
charges $3 for each 30 minutes and a $10.50 flat fee. (Thanks for the question, Claire Q.!)
a.
b.
5.
Create a system of equations to represent the scenario.
How many tutoring classes would give the two plans the same cost? What is the equal
cost? Use mathematics to explain how you determined your answer. Use words, symbols
or both in your explanation.
Which plan costs more for 10 tutoring classes? Use mathematics to justify your answer.
Which plan provides more classes for $200.00? Use mathematics to justify your answer.
Bob is hungry and wants to eat some pizza. He has two different pizzerias to choose from. Pizza
House charges a delivery fee of $6 for the whole order and $16 for each pizza bought. Papa’s
Pizzeria charges no fee for delivery, but $18 for each pizza bought. (Thanks for the question,
Gene!)
a.
b.
4.
Create a system of equations to represent the scenario.
If you want to ride at least 15 rides, where should you go?
If you have $30, where can you go for more rides? Why?
Create a system of equations to represent the scenario.
When will the fee be the same?
Phone Company ASDF has 2 plans. Both of the plans are arranged on a weekly basis. For Plan A,
you have to pay a fixed price of $2 and $2 for every 1 minute of a call you make. For Plan B, you
only have to pay $12 and it gives you unlimited phone calls. (Thanks for the question, Wonu!)
a.
b.
Create a system of equations to represent the scenario.
If you call at least 10 minutes a week, which plan is better? Why?
6.
Shana is looking for an electricity company to use. Wehaveelectricity charges $2.50 per day. The
other company, Electricityplus charges $48 to begin, but charges $0.1 per day. (Thanks for the
question, Marie!)
a.
b.
7.
Mr. Jackson owns a car washing and detailing business. It takes 20 minutes to wash a car and 60
minutes to detail a car. He works at most 8 hours per day and does at most 4 details per day.
a.
b.
c.
8.
Create a system of inequalities to represent the scenario.
Use your GDC to graph the system.
Name one possible solution using appropriate units.
At a racecar driving school, there are safety requirements.
a.
b.
c.
d.
10.
Create a system of inequalities to represent the scenario.
If Mr. Jackson charges $75 for each car he details and $25 for each car wash, what is the
maximum amount of money he could earn in one day?
What is the greatest number of car washes that Mr. Jackson could do in a day? Explain your
reasoning.
An economics class formed a company to sell school supplies. They would like to sell at least 20
notebooks and 50 pens per week, with a goal of earning at least $60 per week.
a.
b.
c.
9.
Create a system of equations to represent the scenario.
If Shana needed electricity for 50 days, which company should she choose?
Create a system of inequalities to represent the scenario.
Use your GDC to graph the system.
Name one possible solution using appropriate units.
Is (50, 180) a solution? Explain.
Ice resurfacers are used for rinks of at lest 1000 square feet and up to 17,000 square feet. The
price ranges from as little as $10,000 to as much as $150,000.
a.
b.
c.
d.
Create a system of inequalities to represent the scenario.
Use your GDC to graph the system.
Name one possible solution using appropriate units.
Is (15,000, 30,000) a solution? Explain.
Standard 3: Communicating Reasoning
1.
2.
Describe the solution of a system of equations if after you added two equations the result was
0 = 0.
3.
Describe the solution of a system of equations if the sum of the equations is 0 = 2.
4.
The solution of a system of equations is (-3, 2). One equation in the system is x + 4y = 5. Find the
second equation for the system. Explain how you derived this equation.