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Resources

Solve a system of equations using any method

First, think about the Loyalist perspective during the Revolutionary War. What emotions or attitudes might they have had about the conflict? Then do the same for a Patriot.

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List at least three adjectives that you believe describe the point of view of a Loyalist. Example adjectives: faithful.

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List at least three adjectives that you believe describe the point of view of a Patriot. Example adjectives: rebellious.

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Writing the Short Story: Based on your understanding of the Loyalist or Patriot perspective, write two paragraphs that tell a short story from the point of view of one of those groups. In your narrative, be sure to:

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Describe your feelings: What emotions are you experiencing as a Loyalist or Patriot? Are you feeling fear, loyalty to the Crown, or conflict over the situation?

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Illustrate your surroundings: What do you see? Are there soldiers marching, local townspeople arguing, or perhaps a Loyalist or Patriot meeting taking place?

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Include dialogue: Use dialogue to show interactions with other characters. This could be a conversation with a family member, a friend who is a Patriot, or a neighbor. Make sure the dialogue reflects your character's Loyalist beliefs and emotions.

A video rental company offers a plan that includes a membership fee of

\$10

\$5

for every DVD borrowed. They also offer a second plan, that costs

\$50

per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that?

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

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Every chemical element goes through natural exponential decay, which means that over time its atoms fall apart. The speed of each element's decay is described by its half-life, which is the amount of time it takes for the number of radioactive atoms of this element to be reduced by half. The half-life of the isotope dubnium

-263

29

seconds. A sample of dubnium

-263

was first measured to have

1024

t

seconds, there were only

32

atoms of this isotope remaining- Write an equation in terms of

t

that models the situation.

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Amy is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges

\$32

for the meal, plus

\$4

per pound for the lobster she picks. At the second restaurant, Amy would pay

\$2

per pound for the lobster, in addition to

\$40

for the meal. Amy realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Amy pay for her dinner? What is the weight? Dinner would cost

\$

at either restaurant if Amy's lobster weighed pounds.

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

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Dr. Kelly, a pediatrician, has

1

annual checkup scheduled next Tuesday, which will fill a total of

52

minutes on her schedule. Next Wednesday, she has

2

annual checkups and

2

sick visits on the schedule, which should take

160

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

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The time allotted is

\_\_\_\_

minutes for an annual checkup and

\_\_\_\_

minutes for a sick visit.

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

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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

3

5

queen beds and used a total of

75

pillows. At another house, she used

12

pillows to spruce up

1

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

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The realtor used

\_\_\_

pillows on every twin bed and

\_\_\_

pillows on every queen bed.

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

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Lola received some gift cards for music and movie downloads for her birthday. Using one of them, she downloaded

1

movie, which cost a total of

\$15

. Using another, she purchased

17

7

movies, which cost a total of

\$139

. How much does each download cost?

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\$

_____ for a song and

\$

_____ for a movie.

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

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The administrative assistant at a software company often provides breakfast when there is a morning meeting. For last week's sales meeting, she purchased

8

dozen doughnuts and

2

dozen croissants, spending a total of

\$68

. In preparation for yesterday's safety meeting, she spent

\$10

1

dozen croissants. Assuming she purchased the items at the same bakery both times, how much does a dozen of each cost?

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A dozen doughnuts costs

\$

\_\_\_\_

, and a dozen croissants costs

\$

\_\_\_\_

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

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Julian and Lee went to an arcade where the machines took tokens. Julian played

4

games of skee ball and

3

games of pinball, using a total of

17

tokens. At the same time, Lee played

1

game of pinball, using up

3

tokens. How many tokens does each game require?

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Every game of skee ball requires

\_\_\_\_

tokens, and every game of pinball requires

\_\_\_\_

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

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Reagan is a hairdresser. Before her lunch break, she colored the hair of

1

89

minutes. After lunch, she gave

1

haircut and colored the hair of

2

193

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

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It takes Reagan

\_\_\_\_

minutes to give a haircut and

\_\_\_\_

minutes to color a client's hair.

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

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

1

large tray, which contain a total of

60

cookies. In the afternoon, she made

5

small trays and

3

large trays, which contain a total of

255

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

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The small tray contains

\_\_\_\_

cookies and the large one contains

\_\_\_\_

Wholesome Pizza surveyed a random sample of

40

Trinity Food Festival attendees about their favorite type of pizza. Of the attendees surveyed,

21

said that sausage pizza was their favorite type of pizza. There are

1600

Trinity Food Festival attendees.

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Based on the data, what is the most reasonable estimate for the number of Trinity Food Festival attendees whose favorite type of pizza is sausage pizza?

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1

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40

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525

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760

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840

Every chemical element goes through natural exponential decay, which means that over time its atoms fall apart. The speed of each element's decay is described by its half-life, which is the amount of time it takes for the number of radioactive atoms of this element to be reduced by half.

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The half-life of the isotope dubnium-

263

29

seconds. A sample of dubnium

-263

was first measured to have

1024

t

seconds, there were only

32

atoms of this isotope remaining.

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Write an equation in terms of

t

that models the situation.

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

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Yesterday, two friends went into a bank to open savings accounts. Regan started by putting

\$7

in her account, and she will deposit an additional

\$363

each week. Devon made no initial deposit, but she will add

\$370

more each week. In a few weeks, the friends will have the same account balance. How many weeks will that take? What is that account balance?

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\_\_\_

weeks, Regan and Devon will each have an account balance of

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

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

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

5

times and the roller coaster

2

times, using a total of

20

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

2

times and the roller coaster

5

times, using a total of

29

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

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\_

tickets to ride the Ferris wheel, and

\_

tickets to ride the roller coaster.

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

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Shawn and Gary 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, Shawn has

25

signatures, and Gary has

20

. Shawn is collecting signatures at an average rate of

8

per day, whereas Gary is averaging

9

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?

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\_

days, Shawn and Gary will each have collected

\_

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

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Two workers in a holiday boutique are filling stockings with small gifts and candy. Beth has already filled

4

stockings and will continue to fill them at a rate of

2

stockings per hour. Aaron, who just arrived to help, can fill

4

stockings per hour. At some point, Aaron will catch up with Beth and they will have completed the same number of stockings. How many stockings will each worker have filled by then? How long will that take?

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The workers will each have filled

\_

\_

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

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Wanda wants to buy a charm bracelet. Rockport Fine Jewelry charges

\$10

per charm, plus

\$96

for the bracelet. Beck Jewelers, in contrast, charges

\$11

\$21

for the bracelet. If Wanda wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. How many charms would that be? What would the total cost of the bracelet be?

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If Wanda adds _____ charms to her bracelet, it will cost

\$

_____ at either shop.

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

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Mrs. Lee is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Yardley Florist charges

\$7

for each smaller arrangement, plus

\$46

for the large centerpiece. Carrie's Flowers, in contrast, charges

\$42

for the large centerpiece and

\$9

per arrangement for the rest. If Mrs. Lee orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be? What would the total cost be?

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If Mrs. Lee orders _____ small arrangements, it will cost

\$

_____ at either shop.

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

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

9

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

2

rows per hour. His mom has finished

7

rows of tomatoes and will continue planting at

3

rows 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 long will that take? How many rows will they each have completed?

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\_

hours, Hanson and his mom will each have planted

\_

rows of vegetables.

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

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

3

small pizzas and

2

large pizzas, the perfect amount for the

14

players going out for pizza. This week, there were

12

players going, so she ordered

2

small pizzas and

2

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

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Each small pizza feeds

\_

people, and each large pizza feeds

\_

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

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

2

small baskets and

10

large baskets, using a total of

194

pieces of fruit. Using wire baskets, the employee assembled

9

small baskets and

10

large baskets, using a total of

243

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?

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The small baskets each include

\_

pieces and the large ones each include

\_

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

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

6

4

necklaces, using a total of

532

beads. For her friends, she assembled

4

7

necklaces, using a total of

697

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

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Valentina uses _____ beads for each bracelet and _____ beads for each necklace.

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

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Yesterday, two friends went into a bank to open savings accounts. Porter started by putting

\$140

in his account, and he will deposit an additional

\$224

each week. Jasmine made no initial deposit, but she will add

\$231

more each week. In a few weeks, the friends will have the same account balance. How many weeks will that take? What is that account balance?

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\_\_\_

weeks, Porter and Jasmine will each have an account balance of

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

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

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The box office at a theater is selling tickets for a series of rock concerts. So far, they have sold

48

balcony tickets and

90

general admission floor tickets for Friday's show, for a total of

\$3,798

in receipts. For Saturday's show,

35

balcony tickets and

81

general admission floor tickets have been sold, equaling

\$3,123

in receipts. How much does each ticket cost?

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A balcony seat ticket costs

\$\_

, and a general admission floor ticket costs

\$\_

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

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A fashion photographer needs to hire a stylist to prepare his models. Santiago charges

\$165

for showing up, plus

\$78

per hour. Jenny charges

\$181

\$74

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

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If the shoot lasted for _____ hours, either stylist would cost

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

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

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Mackenzie is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of

\$16

, and her grandmother has pledged

\$1

per mile. If Mackenzie walks a certain distance, the two donors will end up owing the same amount. What is that distance? How much will each donor owe?

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If Mackenzie walks _____ miles, her mother and grandmother will each owe

\$

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

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A video rental company offers a plan that includes a membership fee of

\$9

\$2

for every DVD borrowed. They also offer a second plan, that costs

\$13

per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? What is that total cost of either plan?

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If a customer rents _____ DVDs, each option costs

\$

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

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While visiting Salem, Gina can pay a flat rate of

\$8

\$1

per hour. For the length of time that Gina wants to park in Salem, the two options are actually equivalent in terms of cost. For how long does Gina want to park? How much will Gina pay?

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\_\_\_\_\_

hours of parking, Gina will pay

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

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

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Jeanette has punch cards for her favorite tea house and her favorite coffee shop. She currently has

10

punches on the tea punch card and

1

punch on the coffee punch card. Given her regular routine, she consistently earns

2

new punches per week on the tea punch card and

3

on the coffee punch card. Before too long, Jeanette will have the same number of punches on each card. How many punches will Jeanette have on each card? How long will that take?

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Jeanette will have

\_

punches on each card in

\_

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

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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

9

small candle holders and

11

large candle holders, using a total of

93

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

12

small candle holders and

11

large candle holders, for a total of

102

candles. How many candles does each candle holder hold?

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Each small candleholder holds

\_

candles, and each large one holds

\_

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

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

17

cars, and Hardin's Autos has sold

11

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

7

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

13

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?

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The dealerships will each have sold _____ cars in _____ days.

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

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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

3

2

queen beds and used a total of

34

pillows. At another house, she used

46

pillows to spruce up

5

2

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

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The realtor used

\_\_\_\_

pillows on every twin bed and

\_\_\_\_

pillows on every queen bed.

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-x + 7y = 7

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x = 7

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-x + 9y = 14

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x = 4

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-9x + 8y = -11

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y = -7

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y = 4

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–4x − 3y = –16

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y = 4

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–8x + 7y = –12

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y = 1

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–2x − 2y = –16

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x + 6y = -4

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x = -10

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x + y = 11

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x = 6

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Solve for the variable

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1

x+12=14

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

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The owner of two hotels is ordering towels. He bought

100

hand towels and

34

bath towels for his hotel in Oak Grove, spending a total of

\$672

. He also ordered

62

hand towels and

45

bath towels for his hotel in Summerfield, spending

\$608

. How much does each towel cost?

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A hand towel costs

\$

_____, and a bath towel costs

\$

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

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Dustin and his workout partner are lifting weights together, doing many sets of each exercise. On a certain exercise, Dustin is using a

32

-pound bar, increasing the amount of weight he lifts by

10

pounds on each set. His partner, meanwhile, started out using a

38

-pound bar and is upping the weight by adding

7

pounds on every set. Eventually, Dustin and his workout partner will be lifting the same amount, and will take turns using the same barbell. How many sets will they have completed? How much weight will they be lifting then?

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After completing

\_\_

sets, they will both be lifting

\_\_

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

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In a paint factory, an old conveyer line has filled

17

barrels of paint, and is filling more at a rate of

8

barrels per minute. A worker just switched on a newer line that can fill

9

barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How long will that take? How many barrels will each line have filled?

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\_\_\_

minutes, both lines will have filled

\_\_\_

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

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The owner of Arlington Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled

11

small arrangements and

11

large arrangements, which took her a total of

88

minutes. After lunch, she arranged

8

small arrangements and

14

large arrangements, which took

100

minutes. How long does it take to assemble each type?

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The florist can assemble a small arrangement in _____ minutes and a large one in _____ minutes.

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

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Mrs. Coleman is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Norwood Florist charges

\$16

for each smaller arrangement, plus

\$33

for the large centerpiece. Adam's Flowers, in contrast, charges

\$41

for the large centerpiece and

\$8

per arrangement for the rest. If Mrs. Coleman orders a certain number of small arrangements, the cost will be the same at either flower shop. What would the total cost be? How many small arrangements would that be?

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The cost will be

\$\_\_\_\_

if Mrs. Coleman orders

\_\_\_

of the small arrangements.

9=\frac{(v+4)}{(v+12)}

Which of the following is a correct interpretation of the expression

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-3-5

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1

\newline

5

on the number line and move

3

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5

on the number line and move

3

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-3

on the number line and move

5

\newline

-3

on the number line and move

5

At the beginning of the year, Adrian's savings account balance was

\$ 28

. Each week, he deposits another

\$ 15

into that account, and he doesn't spend any of his savings.

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Is his savings account balance proportional to the number of weeks since the start of the year?

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1

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