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Solve a system of equations using elimination: word problems

Miguel and his mom are planting vegetables in their garden. Miguel has finished planting

1

row of carrots so far and is planting new rows at a rate of

4

rows per hour. His mom has finished

7

rows of tomatoes and will continue planting at

1

row per hour. Once the pair get to the point where they have finished the same number of rows, they will take a break and decide what to plant next. How many rows will they each have completed?

\newline

Write a system of equations, graph them, and type the solution.

\newline

____ rows

\newline

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Mrs. Griffith, the P.E. teacher, is pairing off students to race against each other. Dominic can run

4 \, \text{meters per second}

, and Seth can run

6 \, \text{meters per second}

. Mrs. Griffith decides to give Dominic a head start of

30 \, \text{meters}

since he runs more slowly. Once the students start running, Seth will quickly catch up to Dominic. How long will that take?

\newline

Write a system of equations, graph them, and type the solution.

\newline

\_\_\_\_

seconds

\newline

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Norma is a hairdresser. Before her lunch break, she gave

1

haircut and colored the hair of

1

client in

106

minutes. After lunch, she gave

1

haircut and colored the hair of

4

clients in

346

minutes. How long does it take for Norma to perform each type of service, assuming the amount of time doesn't vary from client to client?

\newline

It takes Norma

\_

minutes to give a haircut and

\_

minutes to color a client's hair.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

A librarian is expanding some sections of the city library. He buys books at a special price from a dealer who charges one price for any hardback book and another price for any paperback book. For the children's section, Mr. Crosby purchased

28

new hardcover books and

38

new paperback books, which cost a total of

\$506

. He also purchased

58

new hardcover books and

38

new paperback books for the adult fiction section, spending a total of

\$926

. What is the special price for each type of book?

\newline

The special price is

\$\_\_\_\_

for hardcover books and

\$\_\_\_\_

for paperback books.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Gymnasts training for an upcoming competition are practicing their routines for balance beam and floor exercise. During morning practice, Rita practiced her beam routine

3

times and her floor routine

4

times, which took a total of

15

minutes. During afternoon practice, she ran through her her beam routine

8

times and her floor routine

4

times, which took a total of

20

minutes. How long is each routine?

\newline

The beam routine is

\_

minutes long and the floor exercise is

\_

minutes long.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Today's cafeteria specials at a high school in Oakdale are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold

35

turkey sandwiches and

33

chef salads, for a total of

\$134

. During the late lunch,

65

turkey sandwiches and

70

chef salads were sold, for a total of

\$275

. How much does each item cost?

\newline

A turkey sandwich costs

\$\_

, and a chef salad costs

\$\_

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

The cheerleaders from Hampton High School are doing a giftwrapping fundraiser at a clothing store. Yesterday, they wrapped

40

small clothing boxes and

20

large clothing boxes, using a total of

400

feet of wrapping paper. The day before, they wrapped

40

small clothing boxes and

35

large clothing boxes, using a total of

580

feet of gift wrap. How much paper does it take to wrap each size of box?

\newline

Each small box uses

\_

feet of paper and each large one uses

\_

feet.

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Johanna bought

19

items at the college bookstore. The items cost a total of

\$ 35.50

. The pens cost

\$ 0.50

each, the notebooks were

\$ 3.00

each, and the highlighters cost

\$ 1.50

each. She bought

2

more notebooks than highlighters. How many of each item did she buy?

\newline

Use a system of three linear equations to solve the problem.

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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.

\newline

Mario's Pizza just received two big orders from customers throwing parties. The first customer, Ruth, bought

1

deluxe pizza and paid

\$22

. The second customer, Gordon, ordered

9

regular pizzas and

3

deluxe pizzas, paying a total of

\$174

. What is the price of each pizza?

\newline

Each regular pizza costs

\$

_____, and each deluxe pizza costs

\$

______.

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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.

\newline

An employee at a construction company is ordering interior doors for some new houses that are being built. There are

8

one-story houses and

7

two-story houses on the west side of the street, which require a total of

168

doors. On the east side, there are

1

two-story house, which require a total of

16

doors. Assuming that the floor plans for the one-story houses are identical and so are the two-story houses, how many doors does each type of house have?

\newline

Each one-story house has

\_\_\_\_

doors, and each two-story house has

\_\_\_\_

doors.

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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.

\newline

Sandra is working furiously to knit scarves and beanies for a craft fair next weekend. Yesterday she completed

1

scarf, using a total of

8

yards of yarn. The day before, she used

30

yards to knit

3

scarves and

3

beanies. Assuming Sandra is using the same pattern and type of yarn for each scarf and beanie, how much yarn does each project require?

\newline

Each scarf requires

\_\_\_\_

yards of yarn, and each beanie requires

\_\_\_\_

yards.

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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.

\newline

At an ice cream store, a family ordered

1

banana split, paying a total of

\$6

for their order. The next customer ordered

4

banana splits and

6

hot fudge sundaes and paid

\$54

. How much does each item cost?

\newline

A banana split costs

\$\_\_\_\_

and a hot fudge sundae costs

\$\_\_\_\_\_

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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.

\newline

Substitute teachers with Newberg School District get paid by the day, although subs with teaching credentials earn a different amount than subs without credentials. Yesterday,

1

non-credentialed sub taught in the district. That cost the district

\$65

. Today,

8

non-credentialed subs and

4

credentialed subs taught, receiving

\$864

from the district. How much do subs get paid?

\newline

Subs without credentials get paid

\$

_____ per day, and subs with credentials get paid

\$

_____ per day.

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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.

\newline

Friends and family of the bride will be helping assemble centerpieces for the wedding reception. On the right side of the room, there will be

8

round tables and

5

rectangular tables, which will require a total of

31

centerpieces. On the left side, there will be

1

rectangular table, for which they will need to assemble a total of

3

centerpieces. How many centerpieces will be on each table?

\newline

There will be

\_\_\_\_

centerpieces on every round table and

\_\_\_\_

centerpieces on every rectangular one.

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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.

\newline

Two fifth grade classes are attending an amusement park as a field trip. Their teachers purchased the tickets for the class and the parent chaperones. Mrs. Randolph purchased

30

child tickets and

23

adult tickets, which cost a total of

\$1,359

. Mr. Kent purchased

1

adult ticket, paying a total of

\$33

. What are the ticket prices?

\newline

The price of a child ticket is

\$\_\_\_\_

and the price of an adult ticket is

\$\_\_\_\_

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A basketball team stopped at a fast-food restaurant after a game. They are divided into two groups. One group bough

5

chicken sandwiches and

7

hamburgers for a cost of

\$ 24.90

. The second group spent

\$ 28.80

and bought

5

chicken sandwiches and

9

hamburgers. Write a system of equations to represent the situation. Then use it to find the cost of each chicken sandwich and each hamburger?

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Which event is most likely to occur?

\newline

Rolling a number greater than

4

on a twelve-sided die, numbered from

1

12

\newline

Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on green or purple.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

48

tickets.

\newline

Reaching into a bag full of

52

strawberry chews and

8

cherry chews without looking and pulling out a strawberry chew.

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Which event is most likely to occur?

\newline

Rolling a number greater than or equal to

3

on a eight-sided die, numbered from

1

8

\newline

Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on blue or yellow or green or purple.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

41

tickets.

\newline

Reaching into a bag full of

10

strawberry chews and

10

cherry chews without looking and pulling out a strawberry chew.

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Which event is least likely to occur?

\newline

Rolling a number greater than or equal to

6

on a eight-sided die, numbered from

1

8

\newline

Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on yellow.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

79

tickets.

\newline

Reaching into a bag full of

75

strawberry chews and

5

cherry chews without looking and pulling out a strawberry chew.

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Which event is least likely to occur?

\newline

Rolling a number less than

6

on a twelve-sided die, numbered from

1

12

\newline

Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on some color.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

11

tickets.

\newline

Reaching into a bag full of

18

strawberry chews and

2

cherry chews without looking and pulling out a strawberry chew.

Get tutor help

Which event is least likely to occur?

\newline

Rolling a number greater than or equal to

1

on a eight-sided die, numbered from

1

8

\newline

Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on yellow.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

31

tickets.

\newline

Reaching into a bag full of

34

strawberry chews and

6

cherry chews without looking and pulling out a strawberry chew.

Get tutor help

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday, they wrapped

15

small gifts and

33

large gifts, earning a total of

\$357

. Today, they wrapped

35

small gifts and

33

large gifts, and earned

\$437

. How much did they charge to wrap the gifts?

\newline

The organization charges

\_\_\_\_\_

to wrap a small gift and

\_\_\_\_\_

to wrap a large one.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Mrs. McKenzie is shopping for school supplies with her children. Celine selected

1

one-inch binder and

3

two-inch binders, which cost a total of

\$26

. Rose selected

5

one-inch binders and

1

two-inch binder, which cost a total of

\$18

. How much does each size of binder cost?

\newline

A one-inch binder costs

\$\_\_\_\_

, and a two-inch binder costs

\$\_\_\_\_\_\_\_\_\_

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

A boy scout troop is selling Christmas trees at a local tree lot. In the morning, they sold

17

Douglas Fir trees and

23

Noble Fir trees, earning a total of

\$2,009

. In the afternoon, they sold

8

Douglas Fir trees and

5

Noble Fir trees, earning a total of

\$596

. How much does each type of tree cost?

\newline

A Douglas Fir costs _____ and a Noble Fir costs

\$

_____.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Two fifth grade classes are attending an amusement park as a field trip. Their teachers purchased the tickets for the class and the parent chaperones. Mrs. Arnold purchased

23

child tickets and

1

adult ticket, which cost a total of

\$280

. Mr. Norton purchased

25

child tickets and

26

adult tickets, paying a total of

\$977

. What are the ticket prices?

\newline

The price of a child ticket is _____ and the price of an adult ticket is

\$

_____.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

An administrative assistant is making some copies. She made

34

one-sided copies and

11

two-sided copies for the V.P. of Marketing, which took a total of

135

seconds. Next, she made

23

one-sided copies and

42

two-sided copies for the Director of Sales, which took

195

seconds. How long does it take to make each type of copy?

\newline

It takes

\_

seconds to make a one-sided copy and

\_

seconds to make a two-sided copy.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Dr. Patrick, a pediatrician, has

3

annual checkups and

2

sick visits scheduled next Tuesday, which will fill a total of

176

minutes on her schedule. Next Wednesday, she has

2

annual checkups and

1

sick visit on the schedule, which should take

112

minutes. How much time is allotted for each type of appointment?

\newline

The time allotted is

\_

minutes for an annual checkup and

\_

minutes for a sick visit.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Friends and family of the bride will be helping assemble centerpieces for the wedding reception. On the right side of the room, there will be

6

round tables and

2

rectangular tables, which will require a total of

14

centerpieces. On the left side, there will be

6

round tables and

1

rectangular table, for which they will need to assemble a total of

10

centerpieces. How many centerpieces will be on each table?

\newline

There will be

\_

centerpieces on every round table and

\_

centerpieces on every rectangular one.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Liz is creating beaded jewelry to give to her family and friends. For her family, she assembled

7

bracelets and

2

necklaces, using a total of

331

beads. For her friends, she assembled

10

bracelets and

2

necklaces, using a total of

418

beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each?

\newline

Liz uses

\_

beads for each bracelet and

\_

beads for each necklace.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Mrs. Shepherd's grandchildren are participating in a gift wrap sale to raise money for their school. She decided to stock up, so she ordered

2

rolls of reversible paper and

5

rolls of metallic paper from Valeria, spending a total of

\$90

. She also ordered

4

rolls of reversible paper and

5

rolls of metallic paper from Jill, which cost a total of

\$120

. Assuming that rolls of each type are priced the same, what is the price for each kind of paper?

\newline

Rolls of reversible paper cost

\$

_____ each, and rolls of metallic paper cost

\$

_____ each.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

The postal service offers flat-rate shipping for priority mail in special boxes. Today, Jamal shipped

7

small boxes and

4

large boxes, which cost him

\$68

to ship. Meanwhile, Brian shipped

1

small box and

5

large boxes, and paid

\$54

. How much does it cost to ship these two sizes of box?

\newline

Shipping costs

\$\_\_\_\_

for a small box and

\$\_\_\_\_

for a large box.

Get tutor help

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

The Maynard family and the Boyer family are seeing a movie together in the theater. At the concession stand, Mr. Maynard paid

\$18

for

1

large popcorn and

3

large drinks that his family will share. Mrs. Boyer bought

3

large popcorns and

2

large drinks and paid

\$26

. How much does each item cost?

\newline

A large popcorn costs

\$\_\_\_\_

and a large drink costs

\$\_\_\_\_

Get tutor help

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Carson is a server at an all-you-can eat sushi restaurant. At one table, the customers ordered

1

child buffet and

4

adult buffets, which cost a total of

\$110

. At another table, the customers ordered

3

child buffets and

3

adult buffets, paying a total of

\$114

. How much does the buffet cost for each child and adult?

\newline

The cost for a child is

\$\_

, and the cost for an adult is

\$\_

Get tutor help

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

A coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold

14

packages of coffee and

36

packages of tea, for which customers paid a total of

\$386

. The day before,

20

packages of coffee and

36

packages of tea was sold, which brought in a total of

\$428

. How much does each package cost?

\newline

Per package, coffee costs

\$

_____ and tea costs

\$

_____.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

The Ashland High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Walton has requested

80

earth science textbooks and

92

physics textbooks for all of her classes, which costs the department a total of

\$7,744

. Mr. Castro has asked for

80

earth science textbooks and

76

physics textbooks, which will cost a total of

\$6,912

. How much do the textbooks cost?

\newline

Earth science textbooks cost

\$

____ apiece and physics textbooks cost

\$

____ apiece.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Mariana is selling her handmade jewelry online. Yesterday, she sold

9

bracelets and

6

necklaces, for a profit of

\$168

. Today, she made a profit of

\$144

by selling

6

bracelets and

6

necklaces. How much profit does Mariana earn from each piece?

\newline

Mariana earns a profit of

\$\_\_\_\_

from every bracelet and

\$\_\_\_\_

from every necklace.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday, they wrapped

48

small gifts and

29

large gifts, earning a total of

\$318

. Today, they wrapped

19

small gifts and

43

large gifts, and earned

\$315

. How much did they charge to wrap the gifts?

\newline

The organization charges

\$\_\_\_\_

to wrap a small gift and

\$\_\_\_\_

to wrap a large one.

Get tutor help

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

The postal service offers flat-rate shipping for priority mail in special boxes. Today, Pam shipped

9

small boxes and

6

large boxes, which cost her

\$138

to ship. Meanwhile, Donald shipped

3

small boxes and

7

large boxes, and paid

\$116

. How much does it cost to ship these two sizes of box?

\newline

Shipping costs

\$\_\_\_\_

for a small box and

\$\_\_\_\_

for a large box.

Get tutor help

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

The receivers for the Kingwood University football team are practicing running different routes on the field. They have to run a specific distance so that the quarterback knows exactly where to throw the ball. Craig ran

10

post routes and

28

slant routes, which meant he ran a total of

374

yards. Pedro ran

12

post routes and

17

slant routes, which equaled a total of

316

yards. How long is each route?

\newline

A post route is

\_

yards long and a slant route is

\_

yards long.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Tucker gets paid at home for doing extra chores. Last week, he did

6

loads of laundry and

8

loads of dishes, and his parents paid him

\$22

. The week before, he finished

6

loads of laundry and

4

loads of dishes, earning a total of

\$14

. How much does Tucker earn for completing each type of chore?

\newline

Tucker earns

\$\_\_\_\_

per load of laundry and

\$\_\_\_\_

per load of dishes.

Get tutor help

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

A TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be

2

sitcoms and

5

dramas, for a total of

290

minutes of programming, not counting commercials. On Tuesday nights, he has scheduled

4

sitcoms and

1

drama, for a total of

130

minutes of non-commercial programming. All sitcoms have the same length and all dramas have the same length. How long is each type of show?

\newline

Sitcoms are

\_

minutes long and dramas are

\_

minutes long.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

The postal service offers flat-rate shipping for priority mail in special boxes. Today, Dakota shipped

1

small box and

9

large boxes, which cost her

\$121

to ship. Meanwhile, Abby shipped

7

small boxes and

5

large boxes, and paid

\$93

. How much does it cost to ship these two sizes of box?

\newline

Shipping costs

\$\_\_\_\_

for a small box and

\$\_\_\_\_

for a large box.

Get tutor help

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Malone's Bakery sold one customer

1

dozen chocolate cookies and

10

dozen oatmeal cookies for

\$76

. The bakery also sold another customer

10

dozen chocolate cookies and

5

dozen oatmeal cookies for

\$95

. How much do the cookies cost?

\newline

A dozen chocolate cookies cost

\$

_____, and a dozen oatmeal cookies cost

\$

_____.

Get tutor help

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

There are two trails near Sandra's house that she runs regularly, a short loop and a long loop. Last week, she ran

6

short loops and

5

long loops, for a total of

38

miles. This week, she ran

6

short loops and

3

long loops, covering a total of

30

miles. What is the length of each loop?

\newline

The short loop has a length of

\_

miles, and the long loop has a length of

\_

miles.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

At a historical landmark, candles are used to simulate an authentic atmosphere. A volunteer is currently putting new candles in the candle holders. On the east side, he replaced candles in

3

small candle holders and

7

large candle holders, using a total of

65

candles. On the west side, he replaced the candles in

20

small candle holders and

7

large candle holders, for a total of

116

candles. How many candles does each candle holder hold?

\newline

Each small candleholder holds

\_

candles, and each large one holds

\_

candles.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Jackie and her friend Isabelle are each baking apple pies and tarts for a bake sale, using the same recipes. Jackie baked

6

apple pies and

4

apple tarts, using a total of

72

apples. Isabelle made

7

apple pies and

9

apple tarts, which used

110

apples. How many apples does each dessert require?

\newline

An apple pie uses

\_

apples and an apple tart requires

\_

apples.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

The student council at Belleville High School is raising money by selling hot apple cider and hot chocolate at this week's games. They sold

16

apple ciders and

74

hot chocolates at the football game, raising a total of

\$180

. They raised

\$138

at the soccer game by selling

42

apple ciders and

27

hot chocolates. How much is the student council selling each drink for?

\newline

The student council is selling apple cider for

\$

_____ and hot chocolate for

\$

_____.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Gymnasts training for an upcoming competition are practicing their routines for balance beam and floor exercise. During morning practice, Hannah practiced her beam routine

1

time and her floor routine

7

times, which took a total of

15

minutes. During afternoon practice, she ran through her her beam routine

2

times and her floor routine

2

times, which took a total of

6

minutes. How long is each routine?

\newline

The beam routine is

\_

minutes long and the floor exercise is

\_

minutes long.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed

2

small chandeliers and

5

large chandeliers, which weighed a total of

318

pounds. In the second box, he packed

3

small chandeliers and

4

large chandeliers, which had a weight of

295

pounds. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?

\newline

Each small chandelier weighs

\_

pounds and each large one weighs

\_

pounds.

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

There are two trails near Clarence's house that he runs regularly, a short loop and a long loop. Last week, he ran

3

short loops and

4

long loops, for a total of

26

miles. This week, he ran

2

short loops and

4

long loops, covering a total of

24

miles. What is the length of each loop?

\newline

The short loop has a length of

\_

miles, and the long loop has a length of

\_

miles.

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