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Solve a system of equations using elimination: word problems

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

\newline

Pedro is a shoe salesman, and he works on commission. This week, there is a special incentive to sell shoes and boots by a certain company. Yesterday, Pedro sold

1

pair of shoes and

6

pairs of boots, earning

\$105

in commission. Today, he sold

2

pairs of shoes and

8

pairs of boots, earning a total commission of

\$146

. How much does Pedro earn for the sale of each type of footwear?

\newline

Pedro earns

\$

_____ for each pair of shoes and

\$

_____ for each pair of boots.

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

\newline

Scouting troops in Carroll County are putting on a crab feed to raise money for camp. They offer a complete crab dinner as well as a vegetarian option. One troop member sold tickets for

18

crab meals and

38

vegetarian meals, with total receipts of

\$1,546

. Another sold tickets for

30

crab meals and

30

vegetarian meals, bringing in a total of

\$1,710

. How much do the two types of tickets cost?

\newline

A ticket for a crab meal costs

\$\_\_\_\_

, and a ticket for a vegetarian meal costs

\$\_\_\_\_

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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 Cedarburg are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold

44

turkey sandwiches and

67

chef salads, for a total of

\$400

. During the late lunch,

28

turkey sandwiches and

40

chef salads were sold, for a total of

\$244

. 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 an augmented matrix, and fill in the blanks.

\newline

A baseball coach takes his team out for pizza every time they win a game. Not everyone can come each time, so he orders the pizzas based on how many players are coming. After last week's victory, he bought

1

large pizza, the perfect amount for the

5

players going out for pizza. This week, there were

30

players going, so he ordered

5

small pizzas and

5

large pizzas, which was also just the right amount. How many people does each size of pizza feed?

\newline

Each small pizza feeds

\_\_\_\_

people, and each large pizza feeds

\_\_\_\_

people.

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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

Yesterday a chef used

32

eggs to make

4

chocolate souffles and

6

lemon meringue pies. The day before, he made

1

chocolate souffle, which used

5

eggs. How many eggs does each dessert require?

\newline

A chocolate souffle requires

\_\_\_\_

eggs and a lemon meringue pie requires

\_\_\_\_

eggs.

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

\newline

Angie wanted to stock up on drinks for an upcoming party. First, she spent

\$44

12

cases of juice and

10

cases of soda, which is all the store had in stock. A few days later, she returned to the store and purchased an additional

12

cases of juice and

13

cases of soda, spending a total of

\$50

. What is the price of each drink?

\newline

The price for a case of juice is

\$\_\_\_\_

, and the price for a case of soda is

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

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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

22

small gifts and

21

large gifts, earning a total of

\$191

. Today, they wrapped

18

small gifts and

10

large gifts, and earned

\$106

. 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

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

83

earth science textbooks and

65

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

\$7,072

. Mr. Barrett has asked for

83

earth science textbooks and

83

physics textbooks, which will cost a total of

\$8,134

. 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

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

4

haircuts and colored the hair of

1

client in

197

minutes. After lunch, she gave

2

haircuts and colored the hair of

2

clients in

226

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

\newline

It takes Valentina

\_

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

Ivan is trying to incorporate more exercise into his busy schedule. He has several short exercise routines he can complete at home. Last week, he worked out for a total of

102

minutes by doing

1

arm routine and

3

abdominal routines. This week, he has completed

1

arm routine and

4

abdominal routines and spent a total of

132

minutes exercising. How long does each routine last?

\newline

An arm routine takes

\underline{\hspace{3em}}

minutes to complete, and an abdominal routine takes

\underline{\hspace{3em}}

minutes to complete.

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

\newline

To keep in shape, Julie exercises at a track near her home. She requires

62

minutes to do

4

laps running and

10

laps walking. In contrast, she requires

65

minutes to do

5

laps running and

10

laps walking. Assuming she maintains a consistent pace while running and while walking, how long does Julie take to complete a lap?

\newline

Julie takes _____ minutes to run a lap and _____ minutes to walk a lap.

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

\newline

Two friends visited a taffy shop. Tanvi bought

5

kilograms of strawberry taffy and

5

kilograms of banana taffy for

\$65

. Next, Albert bought

5

kilograms of strawberry taffy and

1

kilogram of banana taffy for

\$41

. How much does the candy cost?

\newline

A kilogram of strawberry taffy costs

\$

_____, and a kilogram of banana taffy 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 charitable organization in Newport is hosting a black tie benefit. Yesterday, the organization sold

92

regular tickets and

94

VIP tickets, raising

\$21,408

. Today,

92

regular tickets and

93

VIP tickets were sold, bringing in a total of

\$21,238

. How much do the different ticket types cost?

\newline

A regular ticket costs

\$

_____, and a VIP ticket costs

\$

_____.

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

\newline

Mrs. Chapman sometimes makes her melon salad for special events. When she made it a couple months ago, she used

1

kilogram of honeydew melon and

2

kilograms of watermelon, which cost her

\$9

. Today, she used

2

kilograms of honeydew melon and

1

kilogram of watermelon, spending a total of

\$9

on the melons. Assuming that the prices of the melons haven't changed, how much does a kilogram of each type of melon cost?

\newline

Honeydew melon costs

\$

_____ per kilogram and watermelon costs

\$

_____ per kilogram.

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

\newline

Band students at Silvergrove High School sell candy every year as a fundraiser. Last year, they sold

86

boxes of truffles and

87

boxes of peanut brittle, raising a total of

\$519

. This year, they sold

62

boxes of truffles and

74

boxes of peanut brittle, from which they raised

\$408

. How much does the band earn from each item?

\newline

The band earns

\$\_

from each box of truffles and

\$\_

from each box of peanut brittle.

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

\newline

Two friends visited a taffy shop. Rachel bought

2

kilograms of strawberry taffy and

5

kilograms of banana taffy for

\$43

. Next, Devon bought

1

kilogram of strawberry taffy and

1

kilogram of banana taffy for

\$11

. How much does the candy cost?

\newline

A kilogram of strawberry taffy costs

\$

_____, and a kilogram of banana taffy costs

\$

_____.

Get tutor help

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

\newline

Yesterday a chef used

40

eggs to make

10

chocolate souffles and

10

lemon meringue pies. The day before, he made

2

chocolate souffles and

6

lemon meringue pies, which used

16

eggs. How many eggs does each dessert require?

\newline

A chocolate souffle requires

\_

eggs and a lemon meringue pie requires

\_

eggs.

Get tutor help

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

\newline

A caterer is making cookie trays for upcoming holiday parties. This morning, she made

4

small trays and

1

large tray, which contain a total of

103

cookies. In the afternoon, she made

4

small trays and

2

large trays, which contain a total of

158

cookies. How many cookies do the different sized trays contain?

\newline

The small tray contains

\_

cookies and the large one contains

\_

cookies.

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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

16

packages of coffee and

13

packages of tea, for which customers paid a total of

\$235

. The day before,

33

packages of coffee and

13

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

\$388

. 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

An employee at a party store is assembling balloon bouquets. For a graduation party, he assembled

10

small balloon bouquets and

7

large balloon bouquets, which used a total of

220

balloons. Then, for a Father's Day celebration, he used

84

balloons to assemble

8

small balloon bouquets and

1

large balloon bouquet. How many balloons are in each bouquet?

\newline

The small balloon bouquet uses

\_

balloons and the large one uses

\_

balloons.

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

\newline

Maura is a salon owner. Yesterday, she did

3

haircuts and colored the hair of

5

clients, charging a total of

\$568

. Today, she did

3

haircuts and colored the hair of

2

clients, charging a total of

\$292

. How much does Maura charge for her services?

\newline

Maura charges

\$\_\_\_\_

for a haircut and

\$\_\_\_\_

for a coloring.

Get tutor help

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

\newline

Neil is trying to incorporate more exercise into his busy schedule. He has several short exercise routines he can complete at home. Last week, he worked out for a total of

96

minutes by doing

2

arm routines and

3

abdominal routines. This week, he has completed

2

arm routines and

2

abdominal routines and spent a total of

72

minutes exercising. How long does each routine last?

\newline

An arm routine takes

\_

minutes to complete, and an abdominal routine takes

\_

minutes to complete.

Get tutor help

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

\newline

To keep in shape, Danny exercises at a track near his home. He requires

34

minutes to do

9

laps running and

4

laps walking. In contrast, he requires

40

minutes to do

10

laps running and

5

laps walking. Assuming he maintains a consistent pace while running and while walking, how long does Danny take to complete a lap?

\newline

Danny takes _____ minutes to run a lap and _____ minutes to walk a lap.

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

\newline

Band students at Greenpoint High School sell candy every year as a fundraiser. Last year, they sold

54

boxes of truffles and

75

boxes of peanut brittle, raising a total of

\$420

. This year, they sold

53

boxes of truffles and

83

boxes of peanut brittle, from which they raised

\$431

. How much does the band earn from each item?

\newline

The band earns

\$\_

from each box of truffles and

\$\_

from each box of peanut brittle.

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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

12

Noble Fir trees, earning a total of

\$1,088

. In the afternoon, they sold

9

Douglas Fir trees and

12

Noble Fir trees, earning a total of

\$864

. 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

A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed. In one house, she decorated

5

twin beds and

3

queen beds and used a total of

62

pillows. At another house, she used

34

pillows to spruce up

5

twin beds and

1

queen bed. How many decorative pillows did the realtor arrange on each bed?

\newline

The realtor used

\_

pillows on every twin bed and

\_

pillows on every queen bed.

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

\newline

Two coworkers picked up some writing instruments at the office supply store. Abdul selected

6

boxes of pencils and

8

boxes of ballpoint pens, paying

\$28

. Next, Ezra spent

\$22

5

boxes of pencils and

6

boxes of ballpoint pens. How much does a box of each cost?

\newline

A box of pencils costs

\$

_____, and a box of pens costs

\$

_____.

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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 an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled

9

small baskets and

5

large baskets, using a total of

180

pieces of fruit. Using wire baskets, the employee assembled

2

small baskets and

8

large baskets, using a total of

164

pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each?

\newline

The small baskets each include

\_

pieces and the large ones each include

\_

pieces.

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

\newline

The receivers for the Seaside 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. Damon ran

18

post routes and

29

slant routes, which meant he ran a total of

473

yards. Porter ran

28

post routes and

29

slant routes, which equaled a total of

623

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

One Friday night, two large groups of people called Booneville Taxi Service. The first group requested

2

sedans and

2

minivans, which can seat a total of

18

people. The second group asked for

3

sedans and

2

minivans, which can seat a total of

22

people. How many passengers can each type of taxi seat?

\newline

A sedan can seat _____ people, and a minivan can seat _____ people.

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

\newline

A clothing store is donating socks to various charities. The store gave

5

regular packs and

5

value packs to a homeless shelter, which contained a total of

420

pairs of socks. For foster children, the store donated

5

regular packs and

6

value packs, which equaled

456

pairs. How many pairs of socks are in each pack?

\newline

There are

\_

pairs of socks in each regular pack and

\_

pairs in each value pack.

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