Problem Set and Answer Key
Blueface is going to open up for Kodak Black’s next concert on the Gulf Coast! Amar is trying to make some money by
selling Blueface and Kodak Black T-shirts outside the Coliseum. Each Kodak T-shirt sells for 20 dollars, and each Blueface
T-shirt sells for 15 dollars. Amar made 235 dollars and sold 14 T-shirts. How many Kodak Black shirts did he sell, and
how many Blueface T-shirts did he sell?
20 ( K ) + 15 ( B ) = 235
K + B = 14
K=5
B=9
KK and Caleb want to make the high school basketball gym, so they are going to join a gym over the summer. KK
decided to go to Planet Fitness, which costs $30 to join, and $5 per visit. Caleb decided to go to Club4Fitness, which just
charges $8 per visit. After how many visits have KK and Caleb spent the same amount of money, and how much money
did they spend?
KK: d = 5 v + 30
Caleb: d = 8 v
V = 10
Ariana Grande is coming to North Gulfport Middle School for a fundraising benefit concert! Nevaeh is selling tickets.
This week, she sold 3 kids tickets and 9 adult tickets for a total of $75. Last week, she sold 8 kids tickets and 5 adult
tickets for $67. How much was each adult ticket, and how much was each kids ticket?
3 k + 9 a = 75
8 k + 5 a = 67
K=4
A=7
Solve this system of equations using the graphing method and the substitution method:
5x − 3y = −12
2x + 3y = −9
(-3,-1)
System Of Equations Project
You are going to create a poster demonstrating your skills in solving systems of equations. You will be given a word problem, create
two equations based on the real-world problem, solve the system of equations using graphing AND substitution, and then explain
your findings.
Rubric
A: Exemplary
B: Proficient
C: Developing
D: Beginning
Equations
Student defined the variables
and correctly created both
equations.
Student correctly created both
the variables.
Student made a couple mistakes
when creating their equations.
Equations are random and not
relevant to the problem.
Graphing
Student rewrote both equations
in y=mx+b and graphed
correctly.
Student graphed both lines
correctly.
Student made one or two errors
when graphing the equations.
Student did not graph equations
correctly at all.
Substitution
Student solve the system using
substitution correctly and wrote
solution as a coordinate point.
Student solve the system using
substitution correctly
Student messed up or forgot one
step in solving the system of
equations using substitution.
Student did not substitute
correctly.
Explanations
Student responses were
complete, make sense, and are
grammatically correct.
Student responses were
complete and make sense.
Student responses are not fully
developed and have
grammatical errors.
Student responses are not
relevant, mathematically
correct, or grammatically
correct.
Poster
Poster includes all relevant
information and it neat,
organized, and aesthetically
pleasing.
Poster includes all relevant
information.
Poster is missing one aspect of
the project.
Poster is missing more than one
aspect of the project.
Problem
Blueface is going to open up for Kodak Black’s next concert on the Gulf Coast! Amar is trying to make some money by selling
Blueface and Kodak Black T-shirts outside the Coliseum. Each Kodak T-shirt sells for 20 dollars, and each Blueface T-shirt sells for 15
dollars. Amar made 235 dollars and sold 14 T-shirts. How many Kodak Black shirts did he sell, and how many Blueface T-shirts did
he sell?
Project Components
●
●
●
●
●
●
●
Title, Name, Word Problem
Variables Defined and Two (2) Equations
Graphing Method Solution: Graph must be labeled and numbered. If original equations are in standard form, they must be
re-written in slope-intercept form. (work must be shown). Both lines must be graphed correctly and the solution should be
identified as a coordinate point.
Substitution Method Solution: If both equations are in standard form, one must be rewritten so it has an isolated variable.
All steps of substitution must be shown in a neat and organized fashion (The original substitution to find the first variable,
then the second substitution to find the second variable).
Explanations for both the graphing and substitution method, stating what steps mathematically were taken.
Explanation of solution with regard to the context of the problem.
A paragraph explaining which method the student prefers when solving a system of equation.
Example Poster
System Of Equations Project
You are going to create a poster demonstrating your skills in solving systems of equations. You will be given a word problem, create
two equations based on the real-world problem, solve the system of equations using graphing AND substitution, and then explain
your findings.
Rubric
A: Exemplary
B: Proficient
C: Developing
D: Beginning
Equations
Student defined the variables
and correctly created both
equations.
Student correctly created both
the variables.
Student made a couple mistakes
when creating their equations.
Equations are random and not
relevant to the problem.
Graphing
Student rewrote both equations
in y=mx+b and graphed
correctly.
Student graphed both lines
correctly.
Student made one or two errors
when graphing the equations.
Student did not graph equations
correctly at all.
Substitution
Student solve the system using
substitution correctly and wrote
solution as a coordinate point.
Student solve the system using
substitution correctly
Student messed up or forgot one
step in solving the system of
equations using substitution.
Student did not substitute
correctly.
Explanations
Student responses were
complete, make sense, and are
grammatically correct.
Student responses were
complete and make sense.
Student responses are not fully
developed and have
grammatical errors.
Student responses are not
relevant, mathematically
correct, or grammatically
correct.
Poster
Poster includes all relevant
information and it neat,
organized, and aesthetically
pleasing.
Poster includes all relevant
information.
Poster is missing one aspect of
the project.
Poster is missing more than one
aspect of the project.
Problem
KK and Caleb want to make the high school basketball gym, so they are going to join a gym over the summer. KK decided to go to
Planet Fitness, which costs $30 to join, and $5 per visit. Caleb decided to go to Club4Fitness, which just charges $8 per visit. After
how many visits have KK and Caleb spent the same amount of money, and how much money did they spend?
Project Components
●
●
●
●
●
●
●
Title, Name, Word Problem
Variables Defined and Two (2) Equations
Graphing Method Solution: Graph must be labeled and numbered. If original equations are in standard form, they must be
re-written in slope-intercept form. (work must be shown). Both lines must be graphed correctly and the solution should be
identified as a coordinate point.
Substitution Method Solution: If both equations are in standard form, one must be rewritten so it has an isolated variable.
All steps of substitution must be shown in a neat and organized fashion (The original substitution to find the first variable,
then the second substitution to find the second variable).
Explanations for both the graphing and substitution method, stating what steps mathematically were taken.
Explanation of solution with regard to the context of the problem.
A paragraph explaining which method the student prefers when solving a system of equation.
Example Poster
System Of Equations Project
You are going to create a poster demonstrating your skills in solving systems of equations. You will be given a word problem, create
two equations based on the real-world problem, solve the system of equations using graphing AND substitution, and then explain
your findings.
Rubric
A: Exemplary
B: Proficient
C: Developing
D: Beginning
Equations
Student defined the variables
and correctly created both
equations.
Student correctly created both
the variables.
Student made a couple mistakes
when creating their equations.
Equations are random and not
relevant to the problem.
Graphing
Student rewrote both equations
in y=mx+b and graphed
correctly.
Student graphed both lines
correctly.
Student made one or two errors
when graphing the equations.
Student did not graph equations
correctly at all.
Substitution
Student solve the system using
substitution correctly and wrote
solution as a coordinate point.
Student solve the system using
substitution correctly
Student messed up or forgot one
step in solving the system of
equations using substitution.
Student did not substitute
correctly.
Explanations
Student responses were
complete, make sense, and are
grammatically correct.
Student responses were
complete and make sense.
Student responses are not fully
developed and have
grammatical errors.
Student responses are not
relevant, mathematically
correct, or grammatically
correct.
Poster
Poster includes all relevant
information and it neat,
organized, and aesthetically
pleasing.
Poster includes all relevant
information.
Poster is missing one aspect of
the project.
Poster is missing more than one
aspect of the project.
Problem
Ariana Grande is coming to North Gulfport Middle School for a fundraising benefit concert! Nevaeh is selling tickets.
This week, she sold 3 kids tickets and 9 adult tickets for a total of $75. Last week, she sold 8 kids tickets and 5 adult
tickets for $67. How much was each adult ticket, and how much was each kids ticket?
Project Components
●
●
●
●
●
●
●
Title, Name, Word Problem
Variables Defined and Two (2) Equations
Graphing Method Solution: Graph must be labeled and numbered. If original equations are in standard form, they must be
re-written in slope-intercept form. (work must be shown). Both lines must be graphed correctly and the solution should be
identified as a coordinate point.
Substitution Method Solution: If both equations are in standard form, one must be rewritten so it has an isolated variable.
All steps of substitution must be shown in a neat and organized fashion (The original substitution to find the first variable,
then the second substitution to find the second variable).
Explanations for both the graphing and substitution method, stating what steps mathematically were taken.
Explanation of solution with regard to the context of the problem.
A paragraph explaining which method the student prefers when solving a system of equation.
Example Poster
System Of Equations Project
You are going to create a poster demonstrating your skills in solving systems of equations. You will be given a word problem, create
two equations based on the real-world problem, solve the system of equations using graphing AND substitution, and then explain
your findings.
Rubric
A: Exemplary
B: Proficient
C: Developing
D: Beginning
Equations
Student defined the variables
and correctly created both
equations.
Student correctly created both
the variables.
Student made a couple mistakes
when creating their equations.
Equations are random and not
relevant to the problem.
Graphing
Student rewrote both equations
in y=mx+b and graphed
correctly.
Student graphed both lines
correctly.
Student made one or two errors
when graphing the equations.
Student did not graph equations
correctly at all.
Substitution
Student solve the system using
substitution correctly and wrote
solution as a coordinate point.
Student solve the system using
substitution correctly
Student messed up or forgot one
step in solving the system of
equations using substitution.
Student did not substitute
correctly.
Explanations
Student responses were
complete, make sense, and are
grammatically correct.
Student responses were
complete and make sense.
Student responses are not fully
developed and have
grammatical errors.
Student responses are not
relevant, mathematically
correct, or grammatically
correct.
Poster
Poster includes all relevant
information and it neat,
organized, and aesthetically
pleasing.
Poster includes all relevant
information.
Poster is missing one aspect of
the project.
Poster is missing more than one
aspect of the project.
Problem
Solve this system of equations using the graphing method and the substitution method:
5x − 3y = −12
2x + 3y = −9
Project Components
●
●
●
●
●
●
●
Title, Name, Word Problem
Variables Defined and Two (2) Equations
Graphing Method Solution: Graph must be labeled and numbered. If original equations are in standard form, they must be
re-written in slope-intercept form. (work must be shown). Both lines must be graphed correctly and the solution should be
identified as a coordinate point.
Substitution Method Solution: If both equations are in standard form, one must be rewritten so it has an isolated variable.
All steps of substitution must be shown in a neat and organized fashion (The original substitution to find the first variable,
then the second substitution to find the second variable).
Explanations for both the graphing and substitution method, stating what steps mathematically were taken.
Explanation of solution with regard to the context of the problem.
A paragraph explaining which method the student prefers when solving a system of equation.
Example Poster