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Solve a system of equations using any method: word problems

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

\newline

Two classmates got together over the weekend to do their assigned History reading. Sandra can read

3

pages per minute, while Ronald can read

2

pages per minute. When they met, Sandra had already read

21

pages, and Ronald had already gotten through

50

pages. After a while, they had both read the same number of pages. How long did that take? How many pages had each one read?

\newline

After

\_\_\_

minutes, Sandra and Ronald had each read

\_\_\_

pages.

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

\newline

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

4

bracelets and

10

necklaces, for a profit of

\$212

. Today, she made a profit of

\$260

by selling

10

bracelets and

10

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

\newline

Gabrielle earns a profit of

\$\underline{\hspace{1cm}}

from every bracelet and

\$\underline{\hspace{1cm}}

from every necklace.

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

\newline

This morning, Ben processed two catering orders at the sandwich shop where he works. The first order was for

7

trays of club sandwiches and

5

trays of vegetarian sandwiches, at a cost of

\$103

. The second order, which cost

\$53

, was for

5

trays of club sandwiches and

1

tray of vegetarian sandwiches. How much do the trays cost?

\newline

A tray of club sandwiches costs

\$

_____, and a tray of vegetarian sandwiches costs

\$

_____.

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

\newline

Bernie 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, Bernie sold

6

pairs of shoes and

8

pairs of boots, earning

\$194

in commission. Today, he sold

4

pairs of shoes and

1

pair of boots, earning a total commission of

\$47

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

\newline

Bernie 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 any method, and fill in the blanks.

\newline

Noah and Jane are comparing the international calling plans on their cell phones. On his plan, Noah pays

\$5

just to place a call and

\$2

for each minute. When Jane makes an international call, she pays

\$2

to place the call and

\$5

for each minute. A call of a certain duration would cost exactly the same under both plans. What is the cost? What is the duration?

\newline

Under each plan, a call would cost

\$

_____ if it were

_____ minutes in duration.

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

\newline

Percy and Wyatt started out at their houses and are biking towards each other. Percy started out first, and has already gone

6

kilometers. He bikes at a constant speed of

4

kilometers per hour. Wyatt just left, and rides at

7

kilometers per hour. When the boys meet halfway between their houses, they will continue to the park together. How long will that take? How far will each boy have ridden?

\newline

\_\_\_

hours, both boys will have ridden

\_\_\_

kilometers.

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

\newline

At an ice cream store, a family ordered

3

banana splits and

2

hot fudge sundaes, paying a total of

\$22

for their order. The next customer ordered

3

banana splits and

3

hot fudge sundaes and paid

\$27

. 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 any method, and fill in the blanks.

\newline

The owner of two hotels is ordering towels. He bought

14

hand towels and

41

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

\$521

. He also ordered

50

hand towels and

45

bath towels for his hotel in Yardley, spending

\$745

. 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 any method, and fill in the blanks.

\newline

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

6

regular packs and

4

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

312

pairs of socks. For foster children, the store donated

6

regular packs and

6

value packs, which equaled

354

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

\newline

Wanda is looking for a job cutting hair. One option is self-employment at The Lexington Salon, where she would pay

\$585

per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon

\$9

for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How much would Wanda pay? How many haircuts would that be?

\newline

Wanda would pay

\$

_____ to either salon if she performed _____ haircuts.

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

\newline

The glee club needs to raise money for the spring trip to Europe, so the members are assembling holiday wreaths to sell. Before lunch, they assembled

17

regular wreaths and

11

deluxe wreaths, which used a total of

100

pinecones. After lunch, they assembled

17

regular wreaths and

20

deluxe wreaths, using a total of

154

pinecones. How many pinecones are they putting on each wreath?

\newline

The regular wreaths each have

\_\_\_

pinecones on them, and the large ones each have

\_\_\_

pinecones.

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

\newline

Connor and Fred got in trouble at football practice and have to run laps as a consequence. Connor, who runs at a rate of

2

laps per minute, had completed

4

laps already when he was joined on the track by Fred. Fred's pace is

6

laps per minute. At some point, the two will have run the same distance. How long will that take? How many laps will each boy have run?

\newline

After

\underline{\hspace{2em}}

minutes, Connor and Fred will each have run

\underline{\hspace{2em}}

laps.

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

\newline

Leah owns a cake shop and she is working on two wedding cakes this week. The first cake consists of

5

small tiers and

3

large tiers, which will serve a total of

248

guests. The second one includes

2

small tiers and

1

large tier, which is enough servings for

89

guests. How many guests does each size of tier serve?

\newline

A small tier will serve

\_

guests and a large tier will serve

\_

guests.

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

\newline

Professor Garrett is grading papers in the teachers' lounge. He has already finished grading

16

assignments, and is grading

3

more assignments per hour. His teaching assistant just came in to help him. He can grade at a rate of

5

assignments every hour. At some point, they will be finished and will have graded the same number of papers. How long will that take? How many assignments will they each have graded?

\newline

\_

hours, both Professor Garrett and his assistant will have graded

\_

assignments.

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

\newline

Nolan is going to send some flowers to his wife. Clarksville Florist charges

\$2

per rose, plus

\$25

for the vase. Clara's Flowers, in contrast, charges

\$1

per rose and

\$31

for the vase. If Nolan orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be? How many roses would there be?

\newline

The cost will be

\$\_\_\_\_

if the bouquet contains

\_\_\_\_

roses.

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

\newline

A fashion photographer needs to hire a stylist to prepare her models. Pablo charges

\$183

for showing up, plus

\$72

per hour. Joey charges

\$181

plus

\$74

per hour. The photographer realizes that, given the expected duration of her photo shoot, either stylist would cost her the same amount. What would the cost be? What would the duration be?

\newline

Either stylist would cost

\$

_____ if the shoot lasted _____ hours.

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

\newline

Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent

\$181

10

new shirts and

7

pairs of shorts. The older brother purchased

7

new shirts and

7

pairs of shorts and paid a total of

\$154

. How much did each item cost?

\newline

Each shirt cost

\$

_____, and each pair of shorts cost

\$

_____.

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

\newline

An event organizer is reserving rooms for two company-wide events. For the quarterly meeting this month, she reserved

2

conference rooms and

1

ballroom, which can seat a total of

87

attendees. For safety training next month, she reserved

4

conference rooms and

1

ballroom, which can seat

117

attendees. How many attendees can each room accommodate?

\newline

Each conference room can accommodate

\_\_\_

attendees, and every ballroom can accommodate

\_\_\_

attendees.

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

\newline

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

48

strands of lights to decorate

3

bushes and

3

trees. This afternoon, he strung lights on

4

bushes and

5

trees, using a total of

75

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

\newline

Brian 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 any method, and fill in the blanks.

\newline

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

33

small gifts and

23

large gifts, earning a total of

\$240

. Today, they wrapped

19

small gifts and

35

large gifts, and earned

\$334

. 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 any method, and fill in the blanks.

\newline

Trevor hosts a podcast about computers, and Sharon hosts a podcast about parenting. Both podcasts have a set duration for each episode. Last year, Trevor released

27

episodes and Sharon released

27

episodes, for a total of

6,345

minutes of content. This year, Trevor released

30

episodes and Sharon released

27

episodes, which lasted a total of

6,537

minutes. How long is each episode?

\newline

Each episode of Trevor's podcast is

\_

minutes long, and each episode of Sharon's podcast is

\_

minutes long.

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

\newline

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

5

arrows in the outer ring and

5

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

560

points. Jen went second and got

2

arrows in the outer ring and

5

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

503

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 any method, and fill in the blanks.

\newline

A charitable organization in Castroville is hosting a black tie benefit. Yesterday, the organization sold

92

regular tickets and

88

VIP tickets, raising

\$20,828

. Today,

53

regular tickets and

87

VIP tickets were sold, bringing in a total of

\$18,352

. 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 any method, and fill in the blanks.

\newline

For her parents' anniversary party, Sandra is considering using one of two venues. A hotel in Newport will cost

\$659

for a reservation, plus

\$97

per person. A restaurant in the same city will cost

\$98

per person, in addition to

\$658

for the reservation. In order to make the best decision, Sandra figures out how many attendees it would take to have the venues cost the same amount. What would the total cost be? How many attendees would that be?

\newline

The cost at each venue would be

\$

_____ if the party had _____ attendees.

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

\newline

Mr. Lin, the owner of two car dealerships in Oakland, is holding a contest to see which one can sell the most cars. Oakland Cars has already sold

15

cars, and Lin's Autos has sold

7

cars. Going forward, the salespeople at Oakland Cars think they can sell

7

cars per day, whereas the salespeople at Lin's Autos are aiming for sales of

9

cars per day. If the salespeople's predictions are accurate, it won't be long before the two dealerships are tied. How many cars will each lot have sold? How long will that take?

\newline

The dealerships will each have sold

\_\_

cars in

\_\_

days.

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

\newline

At the Oak Grove Ice Cream Parlor, one group of friends ordered

2

small servings of ice cream and

3

large servings of ice cream for

\$22

. Another group of friends ordered

4

small servings of ice cream and

3

large servings of ice cream for

\$26

. How much does the ice cream cost?

\newline

The ice cream costs

\$\_\_\_\_

for a small serving and

\$\_\_\_\_

for a large serving.

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

\newline

Sparrowtown Photography Studio is taking graduation portraits for students at local schools. Eighth graders from Sparrowtown Elementary School ordered

53

basic portrait packages and

77

deluxe portrait packages, for a total of

\$10,350

. The seniors at Salem High ordered

71

basic portrait packages and

96

deluxe portrait packages, for a total of

\$13,150

. How much does each type of package cost?

\newline

A basic package costs

\$

_____, and a deluxe package costs

\$

_____.

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

\newline

Yesterday a chef used

51

eggs to make

9

chocolate souffles and

8

lemon meringue pies. The day before, he made

1

chocolate souffle and

8

lemon meringue pies, which used

27

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 any method, and fill in the blanks.

\newline

A group of friends are at a baseball game and are purchasing souvenirs. Emmy purchased

1

t-shirt and

3

baseball caps, spending a total of

\$115

. Her Tanvi purchased

3

t-shirts and

4

baseball caps, which cost her a total of

\$195

. Assuming that all of the t-shirts and all of the caps are the same price, what is the price of each?

\newline

Shirts are

\$

_____ apiece and caps are

\$

_____ apiece.

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Write a system of equations to describe the situation below, solve using any method, 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

9

round tables and

11

rectangular tables, which will require a total of

51

centerpieces. On the left side, there will be

9

round tables and

10

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

48

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 any method, and fill in the blanks.

\newline

Amy wants to make scrapbooks with old family photos. An online scrapbooking company charges

\$24

for a basic book and

\$2

per page. Meanwhile, a family friend is willing to make a scrapbook for

\$41

plus

\$1

per page. For a certain number of pages, the price would be equal. How much would that cost? How many pages would that be?

\newline

The scrapbook would cost

\$

_____ if it had _____ pages.

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

\newline

A daycare center in Dover currently has

3

assistant caregivers and

11

senior caregivers. Since demand is high, the owner is going to be hiring

3

assistant caregivers per month and

2

senior caregivers per month. Her goal is to have a larger staff, including an equal number of assistant caregivers and senior caregivers. How many of each type will there be? How long will that take?

\newline

There will be

\_

of each type of caregiver in

\_

months.

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

\newline

Pedro is a plumber, and his coworker Farid is an electrician. Pedro charges customers a fee of

\$108

just to come to their houses and then

\$2

per minute that he is there. Farid also charges a fee of

\$81

for a home visit, plus an additional

\$3

per minute. Last week the coworkers went to a job site together, spent the same amount of time working, and earned the same amount. How much did each one earn? How much time did each one spend working?

\newline

Pedro and Farid each earned

\$

_____ by working for _____ minutes.

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

\newline

Celine and Malik, the boy she was babysitting, were playing basketball together. Her score was

20

points, and his score was

14

points. Celine wanted to make the game more fair, so she called a time-out and modified the rules a bit. Celine explained that, for the rest of the game, she would get

2

points per basket, and Malik would get

4

points per basket. Then they played a bit longer. After the time-out, they both made the same number of baskets and ended up with a tied score. How many baskets did each person make after the time out? How many points did each person have at the end?

\newline

Celine and Malik each made

\_

baskets after the time-out, for a score of

\_

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Write a system of equations to describe the situation below, solve using any method, 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, Quinn practiced her beam routine

3

times and her floor routine

1

time, which took a total of

6

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

2

times and her floor routine

2

times, which took a total of

8

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 any method, and fill in the blanks.

\newline

The drama club is selling gift baskets to raise money for new costumes. During the fall play, they sold a combined

22

regular gift baskets and

7

deluxe gift baskets, earning a total of

\$627

. During the spring musical, they sold

14

regular gift baskets and

2

deluxe gift baskets, earning a total of

\$318

. How much are they charging for the different sized gift baskets?

\newline

The drama club is charging

\$\_\_\_\_

for a regular gift basket and

\$\_\_\_\_

for a deluxe gift basket.

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

\newline

A couple of friends decide to race each other. Mia can run

5 \text{ meters per second}

, whereas Neil can run

8 \text{ meters per second}

. Because she is slower, Mia also gets a head start of

36 \text{ meters}

. Shortly after they start running, Neil will catch up to Mia. How long will that take? How far will Neil have to run?

\newline

It will take

\_\_

seconds for Neil to run

\_\_

meters and catch up to Mia.

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

\newline

The volleyball team and the wrestling team at Westminster High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets

\$4

per car. In addition, they have already brought in

\$73

from past fundraisers. The wrestling team has raised

\$31

in the past, and they are making

\$5

per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take?

\newline

Each team will have raised a total of

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

after washing

\_\_\_\_\_

cars.

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

\newline

Brenda and Eduardo each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Brenda has

20

signatures, and Eduardo has

28

. Brenda is collecting signatures at an average rate of

9

per day, whereas Eduardo is averaging

8

signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?

\newline

\_\_

days, Brenda and Eduardo will each have collected

\_\_

signatures.

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

\newline

Darrell's Bakery recently spent a total of

\$115

on new equipment, and their average hourly operating costs are

\$15

. Their average hourly receipts are

\$16

. The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal? How many hours will that take?

\newline

The bakery's expenses and receipts will both total

\$

_____ after _____ hours.

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

\newline

Clarence and Angie went to an arcade where the machines took tokens. Clarence played

6

games of skee ball and

2

games of pinball, using a total of

12

tokens. At the same time, Angie played

6

games of skee ball and

5

games of pinball, using up

21

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

\newline

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

44

twin-size blankets and

11

queen-size blankets, using a total of

165

meters of fabric. Last week, the members completed

16

twin-size blankets and

32

queen-size blankets, which required

256

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

\newline

A twin-size blanket uses

\_

meters of fabric and a queen-size one uses

\_

meters.

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

\newline

The Harding family is looking to rent a large truck for their upcoming move. With Billy's Moving, they would pay

\$40

for the first day plus

\$7

per additional day. With Wildgrove Rent-a-Truck, in comparison, the family would pay

\$41

for the first day plus

\$6

per additional day. Before deciding on which company to use, Mrs. Harding wants to find out what number of additional days would make the two choices equivalent with regards to cost. What would the total cost be? How many additional days would that be?

\newline

The Harding family would pay

\$\_\_\_\_

either way if they rented the truck for

\_\_\_

additional days.

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

\newline

Vicky works in the shipping department of a toy manufacturer. Toy cars weigh

3

pounds apiece and are shipped in a container that weighs

12

pounds when empty. Toy trucks, which weigh

8

pounds apiece, are shipped in a container weighing

7

pounds. When packed with toys and ready for shipment, both kinds of containers have the same number of toys and the same weight. What is the weight of each container? What is the number of toys?

\newline

Each container weighs

\underline{\hspace{2em}}

pounds and contains

\underline{\hspace{2em}}

toys.

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

\newline

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

2

child buffets and

3

adult buffets, which cost a total of

\$121

. At another table, the customers ordered

3

child buffets and

3

adult buffets, paying a total of

\$138

. 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

\$

_____.

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

\newline

Lillian went to play miniature golf on Monday, when it cost

\$12

to rent the club and ball, plus

\$2

per game. Janelle went Thursday, paying

\$5

per game, plus rental fees of

\$3

. By coincidence, they played the same number of games for the same total cost. How many games did each one play? How much did each one spend?

\newline

Lillian and Janelle each played

\underline{\quad}

games and spent

\$\underline{\quad}

Get tutor help

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

\newline

When Colin does

17

push-ups and

13

sit-ups, it takes a total of

64

seconds. In comparison, he needs

80

seconds to do

20

push-ups and

20

sit-ups. How long does it take Colin to do each kind of exercise?

\newline

It takes Colin

\_\_\_

seconds to do a push-up and

\_\_\_

seconds to do a sit-up.

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

\newline

Madelyn is going to ship some gifts to family members, and she is considering two shipping companies. The first shipping company charges a fee of

\$12

to ship a medium box, plus an additional

\$3

per pound. A second shipping company charges

\$15

for the same size of box, plus an additional

\$2

per pound. At a certain weight, the two shipping methods will cost the same amount. What is that weight? How much will it cost?

\newline

At a weight of

\underline{\hspace{2em}}

pounds, the two shipping methods both cost

\$\underline{\hspace{2em}}

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

\newline

Dylan and Leo are hosting events that are catered by the same company. Dylan plans to have

87

adults and

96

children attend, so the total projected cost of his meals is

\$4,938

. Leo has

70

adults and

96

children on his guest list, so he will pay the caterer

\$4,292

. How much does the caterer charge for each meal?

\newline

Every adult's meal costs

\$

_____, and every child's meal costs

\$

_____.

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

\newline

A camp counselor for a summer day camp sometimes buys lunch for her campers at a nearby fast food restaurant. On Monday, she purchased

1

hamburger kid meal and

3

chicken nugget kid meals, for a total of

\$14

. On Thursday, she spent

\$36

4

hamburger kid meals and

7

chicken nugget kid meals. How much does each type of meal cost?

\newline

Each hamburger meal costs

\$

_____, and each chicken nugget meal costs

\$

_____.

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