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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

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

\$38

for

3

large popcorns and

4

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

3

large popcorns and

3

large drinks and paid

\$33

. How much does each item cost?

\newline

A large popcorn costs

\$\_\_\_\_

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

5

sitcoms and

6

dramas, for a total of

341

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

1

sitcom and

1

drama, for a total of

60

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

A boutique in Arcadia specializes in leather goods for men. Last month, the company sold

87

wallets and

55

belts, for a total of

\$8,287

. This month, they sold

43

wallets and

36

belts, for a total of

\$4,713

. How much does the boutique charge for each item?

\newline

The boutique charges

\$\_\_\_\_

for a wallet, and

\$\_\_\_\_

for a belt.

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Madison competes in a robotics challenge. For one task, she programs her robot to move to locations on a grid. The robot picks up a ball at point

A(-6,3)

and moves it first to point

B(-6,-4)

and then to point

C(-2,-4)

along straight paths. Each unit on the grid represents

1 \mathrm{ft}

. What is the total distance Madison's robot moves with the ball?

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

\newline

Evelyn likes to make desserts for bake sales. Last month, she made

2

batches of brownies and

1

batch of cookies, which called for

9

eggs total. The month before, she baked

2

batches of brownies and

2

batches of cookies, which required a total of

12

eggs. How many eggs did Evelyn use for a batch of each dessert?

\newline

Evelyn uses

\_

eggs to make a batch of brownies and

\_

eggs to make a batch of cookies.

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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

4

small balloon bouquets and

5

large balloon bouquets, which used a total of

116

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

225

balloons to assemble

9

small balloon bouquets and

9

large balloon bouquets. 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

The owner of two hotels is ordering towels. He bought

15

hand towels and

93

bath towels for his hotel in Princeton, spending a total of

\$1,098

. He also ordered

74

hand towels and

72

bath towels for his hotel in Lancaster, spending

\$1,162

. How much does each towel cost?

\newline

A hand towel costs

\$\_\_\_\_

, and a bath towel 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 event planner routinely orders ice sculptures for the corporate events she plans. For an executive dinner in Richmond, she ordered

2

small ice sculptures and

3

large ice sculptures, which cost

\$546

. Then, for a release party in Bluepoint, she ordered

5

small ice sculptures and

3

large ice sculptures, which cost a total of

\$717

. How much does each ice sculpture cost?

\newline

Each small ice sculpture costs

\$\_\_\_\_

, and each large one 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 event planner routinely orders ice sculptures for the corporate events she plans. For an executive dinner in Lakewood, she ordered

4

small ice sculptures and

5

large ice sculptures, which cost

\$871

. Then, for a release party in Danville, she ordered

5

small ice sculptures and

2

large ice sculptures, which cost a total of

\$549

. How much does each ice sculpture cost?

\newline

Each small ice sculpture costs

\$

____, and each large one costs

\$

_____.

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

\newline

Edwin and Keith decided to shoot arrows at a simple target with a large outer ring and a smaller bull's-eye. Edwin went first and landed

1

arrow in the outer ring and

2

arrows in the bull's-eye, for a total of

218

points. Keith went second and got

4

arrows in the outer ring and

2

arrows in the bull's-eye, earning a total of

290

points. How many points is each region of the target worth?

\newline

The outer ring is worth

\_

points, and the bull's-eye is worth

\_

points.

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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 Marshall 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

15

crab meals and

17

vegetarian meals, with total receipts of

\$890

. Another sold tickets for

16

crab meals and

17

vegetarian meals, bringing in a total of

\$921

. 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

Students in a health class are tracking how much water they consume each day. Maria has two reusable water bottles: a small one and a large one. Yesterday, she drank

4

small bottles and

3

large bottles, for a total of

3,030

grams. The day before, she drank

2

small bottles and

3

large bottles, for a total of

2,262

grams. How much does each bottle hold?

\newline

The small bottle holds

\_

grams and the large one holds

\_

grams.

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

\newline

Students in a health class are tracking how much water they consume each day. Melissa has two reusable water bottles: a small one and a large one. Yesterday, she drank

2

small bottles and

4

large bottles, for a total of

2,794

grams. The day before, she drank

1

small bottle and

4

large bottles, for a total of

2,411

grams. How much does each bottle hold?

\newline

The small bottle holds _____ grams and the large one holds _____ grams.

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

\newline

Candice loves riding Ferris wheels and roller coasters. While visiting the Lincoln County Fair, she first went on the Ferris wheel

4

times and the roller coaster

4

times, using a total of

32

tickets. Then, after taking a break and having a snack, Candice went on the Ferris wheel

5

times and the roller coaster

2

times, using a total of

25

tickets. How many tickets does it take to ride each attraction?

\newline

It takes

\_

tickets to ride the Ferris wheel, and

\_

tickets to ride the roller coaster.

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

\newline

A boutique in Salem specializes in leather goods for men. Last month, the company sold

93

wallets and

33

belts, for a total of

\$6,063

. This month, they sold

16

wallets and

13

belts, for a total of

\$1,336

. How much does the boutique charge for each item?

\newline

The boutique charges

\$\_\_\_\_

for a wallet, and

\$\_\_\_\_

for a belt.

Get tutor help

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

\newline

Students in a health class are tracking how much water they consume each day. Victoria has two reusable water bottles: a small one and a large one. Yesterday, she drank

3

small bottles and

4

large bottles, for a total of

116

ounces. The day before, she drank

4

small bottles and

4

large bottles, for a total of

132

ounces. How much does each bottle hold?

\newline

The small bottle holds _____ ounces and the large one holds _____ ounces.

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

\newline

Students in a health class are tracking how much water they consume each day. Javier has two reusable water bottles: a small one and a large one. Yesterday, he drank

2

small bottles and

1

large bottle, for a total of

1,230

grams. The day before, he drank

4

small bottles and

3

large bottles, for a total of

2,938

grams. How much does each bottle hold?

\newline

The small bottle holds

\_

grams and the large one holds

\_

grams.

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

\newline

Aubrey is a salon owner. Yesterday, she did

5

haircuts and colored the hair of

1

client, charging a total of

\$338

. Today, she did

4

haircuts and colored the hair of

1

client, charging a total of

\$289

. How much does Aubrey charge for her services?

\newline

Aubrey charges

\$\_

for a haircut and

\$\_

for a coloring.

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

\newline

The members of a sewing circle are making blankets to give to shelters. This week, they made

48

twin-size blankets and

38

queen-size blankets, using a total of

372

yards of fabric. Last week, the members completed

48

twin-size blankets and

24

queen-size blankets, which required

288

total yards of fabric. How much fabric is used for the different sizes of blankets?

\newline

A twin-size blanket uses

\_

yards of fabric and a queen-size one uses

\_

yards.

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

\newline

The owner of a new restaurant is designing the floor plan, and he is deciding between two different seating arrangements. The first plan consists of

14

tables and

22

booths, which will seat a total of

262

people. The second plan consists of

14

tables and

21

booths, which will seat a total of

252

people. How many people can be seated at each type of table?

\newline

Every table can seat

\_

people, and every booth 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

Mrs. Chen is shopping for school supplies with her children. Anita selected

2

one-inch binders and

5

two-inch binders, which cost a total of

\$29

. Kevin selected

2

one-inch binders and

2

two-inch binders, which cost a total of

\$14

. 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

For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Jill purchased

82

shares in the software company and

82

shares in the biotech firm, which cost a total of

\$5,822

. At the same time, Kate invested a total of

\$5,978

95

shares in the software company and

82

shares in the biotech firm. How much did each share cost?

\newline

Each share in the software company cost

\$\_

, and each share in the biotech firm cost

\$\_

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

\newline

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

6

non-credentialed subs and

3

credentialed subs taught in the district. That cost the district

\$756

. Today,

11

non-credentialed subs and

3

credentialed subs taught, receiving

\$1,151

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 elimination, and fill in the blanks.

\newline

Isaac works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of

43

strands of lights to decorate

5

bushes and

2

trees. This afternoon, he strung lights on

5

bushes and

3

trees, using a total of

52

strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Isaac use on each?

\newline

Isaac decorated every bush with

\_

strands of lights and every tree with

\_

strands.

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

\newline

Students in a health class are tracking how much water they consume each day. Alexandra has two reusable water bottles: a small one and a large one. Yesterday, she drank

2

small bottles and

2

large bottles, for a total of

64

ounces. The day before, she drank

1

small bottle and

2

large bottles, for a total of

51

ounces. How much does each bottle hold?

\newline

The small bottle holds _____ ounces and the large one holds _____ ounces.

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

\newline

Herman loves riding Ferris wheels and roller coasters. While visiting the Union County Fair, he first went on the Ferris wheel

1

time and the roller coaster

2

times, using a total of

11

tickets. Then, after taking a break and having a snack, Herman went on the Ferris wheel

4

times and the roller coaster

2

times, using a total of

20

tickets. How many tickets does it take to ride each attraction?

\newline

It takes

\_

tickets to ride the Ferris wheel, and

\_

tickets to ride the roller coaster.

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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

34

small gifts and

48

large gifts, earning a total of

\$486

. Today, they wrapped

28

small gifts and

50

large gifts, and earned

\$484

. 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

Keenan and Darell went to an arcade where the machines took tokens. Keenan played

10

games of skee ball and

6

games of pinball, using a total of

28

tokens. At the same time, Darell played

8

games of skee ball and

4

games of pinball, using up

20

tokens. How many tokens does each game require?

\newline

Every game of skee ball requires

\_

tokens, and every game of pinball requires

\_

tokens.

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