Algebra
Name: ______________________________
Systems of Equations Word Problems
1.
Terri is applying for summer jobs. She checks the Penny Power and finds two different jobs.
Job A pays $8 an hour. Job B pays $5 an hour plus a signing bonus of $12.
a)
b)
c)
d)
e)
2.
Write a variable definition.
Write an equation which represents the amount of money Terri will earn on Job A.
Write an equation which represents the amount of money Terri will earn on Job B.
Graph the system of equations.
For how many hours will Terri earn the same amount of money at both jobs? Where is this
point on the graph? Label it.
John has ideas for a school fundraiser. His first idea is to have students sell Hershey’s
chocolate bars at $1 each. After writing a letter to the Hershey’s company, the company
agrees to give them $25 for selling their product. John’s second idea is to see Godiva
chocolate bars at $2 each.
a) Write a variable definition.
b) Write an equation which represents the amount of money John will earn for his first idea.
c) Write an equation which represents the amount of money John will earn for his second
idea.
d) Graph the system of equations. Label the intersection point.
e) When is John’s first idea better than his second idea? Explain, in detail, how you came up
with your answer. Use proper mathematical vocabulary in your explanation.
3.
Sarah’s neighbors would like to hire her for babysitting. The Smith’s will pay Sarah $10 an
hour plus a bonus of $25. The Johnson’s will pay Sarah $15 an hour.
a) Write a variable definition.
b) Write an equation which represents the amount of money Sarah will earn with the Smiths’.
c) Write an equation which represents the amount of money Sarah will earn with the
Johnson’s.
d) Graph the system of equations. Label the intersection point.
e) When do the Smiths’ pay more than the Johnson’s?
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4.
Your teacher has asked you to determine which company is the better choice to buy mesh
bags from. Bags-R-Us charges $4.50 per bag with a one-time membership charge of $60.
The Fabulous Bag Shop charges $6.50 per bag with a one-time charge of $8 for shipping.
a)
b)
c)
d)
5.
Write a variable definition.
Write a system of equations to compare each plan.
For how many bags will the two companies cost the same amount?
If your teacher purchases 10 bags, which company is the better buy? Explain, in detail,
how you came up with your answer. Use proper mathematical vocabulary in your
explanation.
Devon’s two favorite aunts send him money every year on his birthday. Devon’s parents
deposit the money into a savings account. Aunt Jeannie given Devon $50 for his first birthday
and $5 every birthday after that. Aunt Martha sends Devon $10 for every birthday.
a)
b)
c)
d)
e)
Write a variable definition.
Write an equation which represents the amount of money Aunt Jeannie gives Devon.
Write an equation which represents the amount of money Aunt Martha gives Devon.
What do the slopes represent in the context of the problem?
On which birthday will Devon have received the same amount of money from both aunts?
Show all work.
f) From which Aunt will Devon have received more money from birth through 5 years? What
about from birth through 15 years? Explain, in detail, how you came up with your answer.
Use proper mathematical vocabulary in your explanation.
6.
Jasmine earns $5.50 per hour for yard work. She also charges a $2 fee for supplies for each
job. Johnny charges $4.25 per hour for yard work and a $5 charge for supplies.
a)
b)
c)
d)
Write a variable definition.
Write an equation which represents the amount of money Jasmine earns at her job.
Write an equation which represents the amount of money Johnny earns at his job.
For how many hours will they need to work at one job to earn the same amount of money?
Show all work.
e) If they work 5 hours at one job, who will have the better deal? What if they work 22 hours?
Explain, in detail, how you came up with your answer. Use proper mathematical
vocabulary in your explanation.
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7.
Susie just got her pilot’s license and wants to rent a plane. The Platinum Plane Company
charges $180 plus $92 per hour to rent a plane. The Plastic Plane Company charges $250
plus $78 per hour.
a)
b)
c)
d)
e)
f)
8.
Trendy T-shirts has decided to manufacture a new design. It will cost $400 plus $7 per shirt to
produce them and Trendy plans to spend $5,000 on advertising. The shirts will sell for $12
each.
a)
b)
c)
d)
e)
9.
Write a variable definition.
Write an equation which represents the amount of money Platinum Plane charges.
Write an equation which represents the amount of money Plastic Plane charges.
For how many hours would the companies charge the same amount? Show all work.
What would be the charge for that number of hours (in part d)? Show all work.
For how many hours would you need to rent a plane to make Plastic Plane the best
choice? Explain, in detail, how you came up with your answer. Use proper mathematical
vocabulary in your explanation.
Write a variable definition.
Write an equation which represents the income.
Write an equation which represents the expenses.
How many t-shirts must be sold to break even? Show all work.
How many t-shirts must be sold to earn a profit of $1,000? (Remember: Profit = Income –
Expenses) Explain, in detail, how you came up with your answer. Use proper
mathematical vocabulary in your explanation.
The launch site for Trigon Balloon, CO is 250 feet above sea level. A pink hot-air balloon is
launched from the site and begins to rise at a rate of 110 ft/min. At the same time, a blue
hot-air balloon 2,200 feet above sea level begins to descent at a rate of 165 ft/min.
a)
b)
c)
d)
e)
f)
Write a variable definition.
Write an equation which represents the height of the pink hot-air balloon.
Write an equation which represents the height of the blue hot-air balloon.
How long will it be until the balloons are at the same elevation? Show all work.
How far apart will the balloons’ elevations be after 12 minutes? Show all work.
Does the problem make sense for the blue balloon to descend for 15 minutes? Why or why
not?
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10.
Students are raising money for Relay for Life by selling soda at school. Plan A is to sell Coca
Cola. For each case sold, your group will make a profit of $5. In addition, Coca Cola will
donate $150 to your fundraiser. Plan B is to sell Pepsi. For each case sold, your group will
make a profit of $6. In addition, Pepsi will donate $100 to your fundraiser.
a)
b)
c)
d)
Write a variable definition.
Write a system of equations to compare each plan of earning money.
What will happen to the students’ earnings after 2 cases of Pepsi are sold? Show all work.
What will happen to the students’ earnings after 4 cases of Coca Cola are sold? Show all
work.
e) At what point will the earnings be the same for Plan A and Plan B. Show all work.
11.
Jessica needs to earn money for the class trip. She can take a job at the local grocery store
on the weekends where the pay rate is $6.25 an hour. If she works at the grocery store, her
grandparents will give her $60 to help offset the cost. Jessica also has the option to babysit
her neighbor’s kids during the week and evenings at a rate of $10 an hour.
a)
b)
c)
d)
Write a variable definition.
Write a system of equations to compare each plan of earning money.
How long will Jessica need to work to earn the same amount at both jobs? Show all work.
If you anticipate that you will need $600 for your trip, how many hours must you work at the
grocery store? Show all work.
e) If you are only able to work 30 hours from now until the class trip, which job would allow
you to make more money? Explain, in detail, how you came up with your answer. Use
proper mathematical vocabulary in your explanation.
12.
Gavin and Buddy are both going to Toronto on their graduation vacation. Gavin is driving with
another friend who is charging him a flat fee of $30 plus $0.50 per miles to cover the cost of
driving expenses. Buddy is taking the bus and his trip will cost $35 plus $0.25 per mile.
a)
b)
c)
d)
Write a variable definition.
Write a system of equations that models both boys’ travel.
After how many hours of traveling will their cost be the same? Show all work.
Will Gavin or Buddy have the better deal at six hours? What about at twelve hours? Show
all work.
e) What do the slope and y-intercepts mean in the context of the problem?
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13.
While on vacation, you and your friends decide to go watch some Major League Soccer
games. At Game 1, you and your friends bought three nachos and two large sodas for a total
of $22.50. At Game 2, you and your friends bought two nachos and three sodas for a total of
$20.
a)
b)
c)
d)
14.
Mrs. Pi is looking for a transportation company to hire for a class field trip to the Franklin
Institute. Safe Vans Company will allow you to use 6 vans and 2 cars, which hold a total of 44
people. Van Fan can supply you with 4 vans and 8 cars, which hold a total of 56 people.
a)
b)
c)
d)
15.
Write a variable definition.
Write a system of equations that will represent the given situation.
How many students can be transported by each van? Show all work.
How many students can be transported by each car? Show all work.
The cost of admission for a group of two adults and six students to Waterland Fun Park is $78.
The cost was $90 for a group containing five adults and three students
a)
b)
c)
d)
e)
16.
Write a variable definition.
Write a system of equations to compare each days spending on food at the game.
Which food item was more expensive? By how much? Show all work.
How much money would you and your friends spend at Game 3 if you both four nachos
and six sodas? Show all work.
Write a variable definition.
Write a system of equations to represent this situation.
Determine the cost of admission for one adult. Show all work.
How much cheaper is the cost of a student compared to an adult? Show all work.
How much would it cost six adults and ten students to attend Waterland Fun Park? Show
all work.
The rocket coaster at Lots-of-Fun Amusement Park has 12 cars, some which hold four people
and some that hold eight people. There is room for 56 people altogether.
a)
b)
c)
d)
Write a variable definition.
Write a system of equations to represent this situation
How many four-passenger cars are there? Show all work.
How many eight-passenger cars are there? Show all work.
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17.
It takes Adrianne 10 minutes to make a black and white drawing and 25 minutes to make a
color drawing. Adrianne completed nine drawings in two hours.
a)
b)
c)
d)
18.
Mr. Fibonacci’s math test contains 25 problems. Some questions are worth two points, others
are worth three points. The total test is worth 60 points.
a)
b)
c)
d)
19.
Write a variable definition.
Write a system of equations to represent this situation.
How many 2-point questions are there? Show all work.
What’s the highest score a student can receive if they left half of the 3-point questions
blank? Explain, in detail, how you came up with your answer. Use proper mathematical
vocabulary in your explanation.
Lucas spent $24.75 on a dozen flowers for mother’s day. He bought a mixture of roses and
daises. The roses cost $2.50 each and the daises were $1.75 each.
a)
b)
c)
d)
20.
Write a variable definition.
Write a system of equations to represent this situation.
How many black and white drawings did Adrianne make? Show all work.
How many colored drawings did Adrianne make? Show all work.
Write a variable definition.
Write a system of equations to represent this situation.
How many roses did Lucas buy his mom? Show all work.
How many daises did Lucas buy his mom? Show all work.
A jar contains nickels and quarters. The jar has a total of 20 coins, worth $2.60.
a)
b)
c)
d)
Write a variable definition.
Write a system of equations to represent this situation.
How many nickels are in the jar? Show all work.
How many quarters are in the jar? Show all work.
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21.
The number of calories in a chocolate kiss is twenty less than twice the amount of calories in a
caramel cluster. Three kisses and four clusters together have 360 calories.
a)
b)
c)
d)
22.
Derek is putting a fence around his garden. The width of his fence is five feet less than twice
the length. The perimeter of the garden is 92 feet.
a)
b)
c)
d)
23.
Write a variable definition.
Write a system of equations to represent this situation.
How wide is Derek’s garden? Show all work.
What is the area of Derek’s garden? Show all work.
Grace is eight years older than her brother, Pete. The sum of their ages is 24.
a)
b)
c)
d)
24.
Write a variable definition.
Write a system of equations to represent this situation.
How many calories are in a caramel cluster? Show all work.
If John ate five chocolate kisses and eight caramel clusters, how many calories did he
intake? Explain, in detail, how you came up with your answer. Use proper mathematical
vocabulary in your explanation.
Write a variable definition.
Write a system of equations to represent this situation.
How old is Grace? Show all work.
How old is Pete? Show all work.
Elizabeth met 24 cousins at a family reunion. The number of male cousins was six less than
twice the number of female cousins.
a)
b)
c)
d)
Write a variable definition.
Write a system of equations to represent this situation.
How many female cousins were there? Show all work.
How many male cousins were there? Show all work.
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25.
Juanita bought two books and a mesh bag at the school store for $26. Each book is eight less
than a mesh bag.
a)
b)
c)
d)
26.
Two angles are complementary. One angle is ten more than three times the other.
a)
b)
c)
d)
27.
Write a variable definition.
Write a system of equations to represent this situation.
How much did a mesh bag cost? Show all work.
How much did each book cost? Show all work.
Write a variable definition.
Write a system of equations to represent this situation.
How big is the smaller angle? Show all work.
How big is the larger angle? Show all work.
The sum of two numbers is 50. The first number is 43 less than twice the second.
a) Write a variable definition.
b) Write a system of equations to represent this situation.
c) What are the two numbers? Show all work.
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