Systems of Equations: Word Problems Project!!!
A.REI.10, A.REI.12
Materials:
 Word Problem
 Pencil
 Graph Paper
 Markers/Color Pencils
 Paper: Copy Paper (preferred) or Notebook Paper or Construction paper
Your task:
1. Sign up for word problem #1-31. One sign-up per student. First come, first serve. This must be done
by Wednesday, October 30th.
2. Write a system of equations to model your word problem. This must be done and checked by Mrs.
Smith-Pouncy no later than Friday, November 1st.
3. Set up your equations and solve using 3 different methods. (graphing, substitution, elimination) Clearly
identify each method and show each step for the method.
4. Analyze how to solve a system of equation (“the big picture”) and come up with key facts to help other
students. Write out your theory. Make sure it is well written. Give examples if needed.
5. FINAL PRODUCT IS DUE NO LATER THAN: Friday, November 8th.
How you will present it:
You will make a 7-page. Your job is to do the following:
1. Make a cover with a creative title and illustrations/clip art that refer to your problem. On this cover
you will include your name (first and last) and period.
2. The first inside page will have the complete problem written out. You will define your variables (say
what your two variables stand for) and write your two equations.
3. The second inside page will have:
a. FRONT of PAGE— All work showing how you got the points needed to graph each equation.
b. BACK of PAGE-- Piece of graph paper glued on it. You will graph your system of equations.
Everything should be drawn with a straightedge and it should be very crisp and clean looking.
You will be responsible for drawing your x- and y-axises on the graph paper. Clearly label each
line and the solution to your system on your graph. Explain what your solution means in a
sentence. Hint: Graph your system on the graph paper first, and then glue it into your book
when it is perfect and complete. Please feel free to use color pencils or markers to add a design
element.
4. The third inside page will have the system using the Elimination method. Solve your system using this
method. Show each step neatly. Show your solution checked. Clearly mark/label your solution. Hint:
Double and triple-check your work to make sure you didn't make any mistakes. Explain what your
solution means in a sentence. Do all your work on a scratch piece of paper first and then neatly copy the
work into your book.
5. The fourth inside page will show your system solved using the Substitution Method. Show your work
step by step. Show your solution. Clearly mark/label your solution. Hint: Double and triple-check your
work to make sure you didn't make any mistakes. Explain what your solution means in a sentence. Do
all your work on a scratch piece of paper first and then neatly copy the work into your book.
6. The fifth inside page will be a list neatly written by you. In this list you will write at least FOUR KEY
FACTS that an Algebra I student must know if they are going to write, graph, solve, and check a system
of equations.
7. The last page should be the Comments & Concerns and Rubric page.
***Your Project can be typed and printed.
COMMENTS & CONCERNS
Answer the following questions fully and completely ON THE BACK OF THIS SHEET OF PAPER. Please do not
attach another sheet of paper. Write neatly and clearly.
1. What part of this project did you like the most? Why?
2. What part of this project did you like the least? Why?
3. What part of this project was most troublesome for you? Why?
4. What part of this project was the easiest for you? Why?
5. What suggestions/advice would you give to another student who had to complete this project?
6. What changes would you want made to your project if you had to complete it again?
RUBRIC
_______5 points—
Booklet, put together neatly and nicely
_______5 points—
Cover Page with creative title and illustrations pertaining to the problem
_______15 points—
1st inside page
3 pts-- problem written out neatly
3 pts-- variables defined
9 pts-- system of equations written and correct
_______25 points—
2nd inside page—Graphing Method
Front of Page:
12 pts-- work shown
Back of Page:
5 pts-- system graphed and labeled correctly
(neat with clear solution)
3 pts-- Solution explained in a sentence.
_______15 points—
3rd inside page—Elimination method
12 pts-- systems solved using the elimination method correctly
(neat with clear solution)
3 pts-- Solution explained in a sentence.
_______15 points—
4th inside page—Substitution Method
12 pts-- systems solved using the elimination method correctly
(neat with clear solution)
3 pts-- Solution explained in a sentence.
_______8 points—
5th inside page—
8 pts-- FOUR KEY FACTS.
(neatly written, thoughtful, complete, and accurate)
_______7 points—
Comments and Concerns completed neatly and fully done.
Timing subtraction/bonus __________(+10 pts added to grade for turned in early, -10 pts for each day turned in
late, -10 for an incomplete assignment with necessary deductions from rubric)
I am looking for: Color, Neatness, Organization, Thoughtfulness, Crisp 'n Clean looking, and ABOVE ALL PERFECT
CORRECTNESS OF WORK!
PROBLEMS YOU CAN CHOOSE FROM:
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Kendra owns a restaurant. She charges $1.50 for 2 eggs and one
piece of toast, and $.90 for one egg and one piece of toast. Write
and graph a system of equations to determine how much she
charges for each egg and each piece of toast. Let x represent the
number of eggs and y the number of pieces of toast.
The length of a rectangle is 3 centimeters more than 3 times the
width. If the perimeter of the rectangle is 46 centimeters, find the
dimensions of the rectangle.
The length of a rectangle is 2 cm more than four times the width.
If the perimeter of the rectangle is 84 cm, what are its
dimensions?
The sum of two numbers is 82. Their difference is 24. Write a
system of equations that describes this situation. Solve by
elimination to find the two numbers.
Sharon has some one-dollar bills and some five-dollar bills. She
has 14 bills. The value of the bills is $30. Solve a system of
equations using elimination to find how many of each kind of bill
she has.
A jar containing only nickels and dimes contains a total of 60
coins. The value of all the coins in the jar is $4.45. Solve by
elimination to find the number of nickels and dimes that are in
the jar.
An ice skating arena charges an admission fee for each child plus a
rental fee for each pair of ice skates. John paid the admission fees
for his six nephews and rented five pairs of ice skates. He was
charged $32.00. Juanita paid the admission fees for her seven
grandchildren and rented five pairs of ice skates. She was charged
$35.25. What is the admission fee? What is the rental fee for a
pair of skates?
Mrs. Huang operates a soybean farm. She buys many supplies in
bulk. Often the bulk products need to be custom mixed before
Mrs. Huang can use them. To apply herbicide to a large field she
must mix a solution of 67% herbicide with a solution of 46%
herbicide to form 42 liters of a 55% solution. How much of the
67% solution must she use?
You decide to market your own custom computer software. You
must invest $3,255 for computer hardware, and spend $2.90 to
buy and package each disk. If each program sells for $13.75, how
many copies must you sell to break even?
A motorboat can go 8 miles downstream on a river in 20 minutes.
It takes 30 minutes for the boat to go upstream the same 8 miles.
Find the speed of the current.
Mike and Kim invest $14,000 in equipment to print yearbooks for
schools. Each yearbook costs $7 to print and sells for $35. How
many yearbooks must they sell before their business breaks even?
A movie theater sells tickets for $9.00 each. Senior citizens receive
a discount of $3.00. One evening the theater sold 636 tickets and
took in $4974 in revenue. How many tickets were sold to senior
citizens? How many were sold to “moviegoers” who were not
senior citizens?
At a high school championship basketball game 1200 tickets were
sold. Student tickets cost $1.50 each and adult tickets cost $5.00
each. The total revenue collected for the game was $3200. How
many student tickets were sold? How many adult tickets were
sold?
The treasurer of the student body at a college reported that the
receipts from a recent concert totaled $916. Furthermore, he
announced that 560 people had attended the concert. Students
were charged $1.25 each for admission to the concert, and adults
were charged $2.25 each. How many adults attended the
concert?
Five hundred tickets were sold for a Saturday evening
performance of a play. The tickets cost $7.50 for adults and $4.00
for children. A total of $3312.50 was received for all the tickets
sold that Saturday evening. How many adults attended the play?
A landscaping company placed two orders with a nursery. The
first order was for 13 bushes and 4 trees, and totaled $487. The
second order was for 6 bushes and 2 trees, and totaled $232. The
bills do not list the per-item price. What were the costs of one
bush and of one tree?
A test has twenty questions worth 100 points. The test consists of
True/False questions worth 3 points each and multiple choice
18.
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questions worth 11 points each. How many multiple choice
questions are on the test?
Margie is responsible for buying a week's supply of food and
medication for the dogs and cats at a local shelter. The food and
medication for the dogs costs twice as much as those supplies for
the cats. She needs to feed 164 cats and 24 dogs. Her budget is
$4240. How much can Margie spend on each dog for food and
medication?
Kristen spent $121 on shirts. Fancy shirts cost $28 and plain shirts
cost $15. If she bought a total of 7 shirts, then how many of each
kind did she buy?
A class of 195 students went on a field trip. They took 7 vehicles,
some cars and some buses. Find the number of cars and buses
taken if each car holds 5 students and each bus holds 45 students.
All 231 students in the Math Club went on a field trip. Some
students rode in vans, which hold 7 students each, and some
students rode in buses, which hold 25 students each. How many
of each type of vehicle did they use if there were 15 vehicles
total?
At Elisa's Printing Company LLC there are two kinds of printing
presses: Model A, which can print 70 books per day, and Model B,
which can print 55 books per day. The company owns 14 total
printing presses and this allows them to print 905 books per day.
How many of each type of press do they have?
A woman owns 21 pets. Each of her pets is either a cat or a bird. If
the pets have a total of 76 legs, and assuming that none of the
bird's legs are protruding from any of the cats' jaws, how many
cats and how many birds does the woman own?
The Lopez family had a rectangular garden with a 20 foot
perimeter. They enlarged their garden to be twice as long and
three feet wider than it was originally. They had to, since their
cherry tomato plants were getting out of control. The enlarged
garden has a 40 foot perimeter. What were the dimensions of the
original garden?
The school that Stefan goes to is selling tickets to a choral
performance. On the first day of ticket sales the school sold 3
senior citizen tickets and 1 child ticket for a total of $38. The
school took in $52 on the second day by selling 3 senior citizen
tickets and 2 child tickets. Find the price of a senior citizen ticket
and the price of a child ticket.
Flying to Kampala with a tailwind a plane averaged 158 km/h. On
the return trip the plane only averaged 112 km/h while flying back
into the same wind. Find the speed of the wind and the speed of
the plane in still air.
A boat traveled 210 miles downstream and back. The trip
downstream took 10 hours. The trip back took 70 hours. What is
the speed of the boat in still water? What is the speed of the
current?
The state fair is a popular field trip destination. This year the
senior class at High School A and the senior class at High School B
both planned trips there. The senior class at High School A rented
and filled 8 vans and 8 buses with 240 students. High School B
rented and filled 4 vans and 1 bus with 54 students. Every van had
the same number of students in it as did the buses. Find the
number of students in each van and in each bus.
Brenda's school is selling tickets to a spring musical. On the first
day of ticket sales the school sold 3 senior citizen tickets and 9
child tickets for a total of $75. The school took in $67 on the
second day by selling 8 senior citizen tickets and 5 child tickets.
What is the price each of one senior citizen ticket and one child
ticket?
Matt and Ming are selling fruit for a school fundraiser. Customers
can buy small boxes of oranges and large boxes of oranges. Matt
sold 3 small boxes of oranges and 14 large boxes of oranges for a
total of $203. Ming sold 11 small boxes of oranges and 11 large
boxes of oranges for a total of $220. Find the cost each of one
small box of oranges and one large box of oranges.
A boat traveled 336 miles downstream and back. The trip
downstream took 12 hours. The trip back took 14 hours. What is
the speed of the boat in still water? What is the speed of the
current?