Resources

Resources

Solve a system of equations using substitution

Brendan has punch cards for his favorite tea house and his favorite coffee shop. He currently has

6

punches on the tea punch card and

2

punches on the coffee punch card. Given his regular routine, he consistently earns

1

new punch per week on the tea punch card and

3

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

\newline

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

\newline

\newline

Hunter and Eva each opened a savings account on the same day. Hunter started by putting

\$200

in his account, and he will deposit an additional

\$150

each week. Eva made an initial deposit of

\$600

, and she will add

\$50

more each week. Eventually, Hunter and Eva will each have the same amount saved. How many weeks will that take?

\newline

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

\newline

\_\_\_\_

\newline

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

\newline

Molly has been planting young trees in his garden. The maple tree that is

95

centimeters tall is growing

9

centimeters per month, whereas the oak tree that is

99

centimeters tall is growing

7

centimeters per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?

\newline

The two trees will both be ◻ centimeters tall in ◻ months.

Solve using substitution.

\newline

6x + 7y = 16

\newline

y = 10

\newline

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

\newline

Isaiah and his little sister are saving up money to buy a joint birthday present for their mother. Isaiah already has

\$24

saved and plans to save

\$14

per week from his allowance. His sister has

\$16

saved so far and will save

\$18

per week from hers. The two siblings will soon have saved the same amount towards their mother's gift. How long will that take? How much will each one have saved?

\newline

\_\_\_

weeks, Isaiah and his sister will each have saved

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

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

\newline

Reggie and his good buddy Isaiah are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Reggie has already finished

5

oil changes today, and can complete more at a rate of

3

oil changes per hour. Isaiah just came on shift, and can finish

4

oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How long will that take? How many oil changes will Reggie and Isaiah each have done?

\newline

\_

hours, both men will have completed

\_

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

\newline

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

17

cars, and Livingston's Autos has sold

7

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

7

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

12

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

\newline

\_

days, the dealerships will each have sold

\_

A concert sold general admission tickets for

\$47.50

and lowerlevel seating for

\$97.50

995

tickets sold took in

\$68,762.50

How many seats were sold for general admission and how man seats were sold for lower-level seating?

\newline

470

seats for general admission and

525

seats for lower level

\newline

290

seats for general admission and

705

seats for lower level

\newline

565

seats for general admission and

430

seats for lower level

\newline

515

seats for general admission and

480

seats for lower level

Naomi wants to take fitness classes at a nearby gym, but she needs to start by selecting a membership plan. With the first membership plan, Naomi can pay

\$54

per month, plus

\$1

for each group class she attends. With the second membership plan, she'd pay

\$12

\$3

\newline

If Naomi attends a certain number of classes in a month, the two membership plans end up costing the same total amount. How many classes per month does that take? What is that total amount Naomi will pay per month for a membership and that many classes?

\newline

If Naomi attends

\_\_\_\_

classes per month, she will pay

\$\_\_\_\_

total each month for either membership plan.

A pencil case contains only blue, purple and pink pencils.

\newline

The ratio of blue pencils to purple pencils is

14: 9

\newline

The ratio of purple pencils to pink pencils is

1: 3

\newline

Calculate the percentage of pencils that are pink.

\newline

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

1

share in the software company, which cost a total of

\$38

. At the same time, Daniel invested a total of

\$3,312

33

shares in the software company and

21

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

\$

\_\_\_\_

, and each share in the biotech firm cost

\$

\_\_\_\_

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

\newline

McCoy's Bakery sold one customer

1

dozen chocolate cookies for

\$7

. The bakery also sold another customer

4

dozen chocolate cookies and

8

dozen oatmeal cookies for

\$76

. How much do the cookies cost?

\newline

A dozen chocolate cookies cost

\$

_____, and a dozen oatmeal cookies cost

\$

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

\newline

Two friends visited a taffy shop. Colin bought

4

kilograms of strawberry taffy and

1

kilogram of banana taffy for

\$25

. Next, Keenan bought

1

kilogram of banana taffy for

\$5

. How much does the candy cost?

\newline

A kilogram of strawberry taffy costs

\$

_____, and a kilogram of banana taffy costs

\$

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

\newline

Manuel often orders party trays from his favorite Mexican food restaurant for company events. For a recent company party, he spent

\$34

1

burrito platter. For a company meeting, he spent

\$123

3

burrito platters and

1

taco platter. How much does each type of platter cost?

\newline

Each burrito platter costs

\$\_\_\_\_

and each taco platter costs

\$\_\_\_\_

f) Dailin is mowing lawns at

\$ 40

per hour to save for a new bike which is

\$ 670

65 \%

of his lawn mowing money and his dad will give him

\$ 3

\$ 2

\newline

How many hours will he need to mow lawns to save enough money for his bilke?

Solve using substitution.

\newline

\begin{array}{l} 2 x-5 y=-16 \\ x=7 \end{array}

\newline

(\square,\square)

The ratio of the number of children to the number of adults at an exhibition is

7: 2.26

children leave the exhibition.

20

more adults arrive at the exhibition. The ratio of the number of children to the number of adults then becomes

1: 2

. How many people are there at the exhibition at first?

The Johnson family is planning a summer road trip to meet up with some friends who live

730

miles away from them. The family takes a scenic route through the winding roads of the countryside. They expect to complete the road in trip in three days. The distances and average speeds for the first two days of the trip are shown.

\newline

1

5

hours at an average speed of

45

\newline

2

8

hours at an average speed of

35

\newline

The average speed on the third day is

45

miles per hour.

\newline

Write an equation using letters and numbers to determine how many more hours it will take the Johnson family to reach their destination. Explain your reasoning.

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

\newline

The Hillsboro Tigers are having team shirts made. One option is to pay Clarence's Tees a

\$ 50

setup fee and then buy the shirts for

\$ 5

each. Another option is to go to City Printing, paying

\$ 36

for a setup fee and an additional

\$ 12

per shirt. The team parent in charge of the project notices that, with a certain number of shirts, the two options have the same cost. How many shirts is that? What is the cost?

\newline

If the Tigers have

\square

shirts made, the cost is

\$ \square

Solve the system of equations using SUBSTITUTION.

\newline

\begin{array}{l} y=2 x+5 \\ y=x+7 \end{array}

Solve using substitution.

\newline

-10x + 10y = -20

\newline

x = 4

\newline

Solve using substitution.

\newline

-2x + y = -14

\newline

x = 10

\newline

Solve using substitution.

\newline

-4x + 5y = -14

\newline

x = -9

\newline

Solve using substitution.

\newline

5x + 6y = -14

\newline

x = 8

\newline

Solve using substitution.

\newline

8x + 6y = 14

\newline

y = 9

\newline

Solve using substitution.

\newline

-6x - 8y = -6

\newline

y = 3

\newline

Solve using substitution.

\newline

-7x + 5y = -13

\newline

x = -1

\newline

Solve using substitution.

\newline

-9x + 8y = -15

\newline

y = 6

\newline

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

\newline

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

35

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

2

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

41

-pound bar and is upping the weight by adding

1

pound on every set. Eventually, Hunter 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?

\newline

After completing

\_\_

sets, they will both be lifting

\_\_

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

\newline

Vijay and his good buddy Doug are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Vijay has already finished

3

oil changes today, and can complete more at a rate of

3

oil changes per hour. Doug just came on shift, and can finish

4

oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How long will that take? How many oil changes will Vijay and Doug each have done?

\newline

\_

hours, both men will have completed

\_

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

\newline

Shannon, an office manager, needs to find a courier to deliver a package. The first courier she is considering charges a fee of

\$15

\$1

per pound. The second charges

\$6

\$4

per pound. Shannon determines that, given her package's weight, the two courier services are equivalent in terms of cost. How much will it cost? What is the weight?

\newline

The two couriers both cost

\$

_____ at a package weight of _____ pounds.

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

\newline

Bobby has been planting young trees in his garden. The maple tree that is

14

inches tall is growing

2

inches per month, whereas the oak tree that is

10

inches tall is growing

3

inches per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?

\newline

The two trees will both be

\_

\_

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

\newline

Two sisters have decided to watch all the episodes of a popular TV show on DVD. Eva has already watched

2

episodes and will continue to watch the show at a rate of

2

episodes per day. Olivia, who hasn't yet seen the show, will start watching

4

episodes per day. Once the two sisters get to the point where they have watched the same number of episodes, they plan to finish the series together. How long will that take? How many episodes will each sister have watched at that point?

\newline

\_

days, the sisters will each have watched

\_

episodes of the show.

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

\newline

Two sisters have decided to watch all the episodes of a popular TV show on DVD. Sophia has already watched

3

episodes and will continue to watch the show at a rate of

1

episode per day. Jenny, who hasn't yet seen the show, will start watching

4

episodes per day. Once the two sisters get to the point where they have watched the same number of episodes, they plan to finish the series together. How long will that take? How many episodes will each sister have watched at that point?

\newline

\_

days, the sisters will each have watched

\_

episodes of the show.

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

\newline

For his parents' anniversary party, Clarence is considering using one of two venues. A hotel in Millersburg will cost

\$736

for a reservation, plus

\$26

per person. A restaurant in the same city will cost

\$31

per person, in addition to

\$616

for the reservation. In order to make the best decision, Clarence 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.

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

\newline

Farid and his good buddy Xavier are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Farid has already finished

7

oil changes today, and can complete more at a rate of

1

oil change per hour. Xavier just came on shift, and can finish

2

oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How long will that take? How many oil changes will Farid and Xavier each have done?

\newline

\_

hours, both men will have completed

\_

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

\newline

Darnel has been planting young trees in her garden. The maple tree that is

57

centimeters tall is growing

7

centimeters per month, whereas the oak tree that is

63

centimeters tall is growing

5

centimeters per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?

\newline

The two trees will both be

\_

centimeters tall in

\_

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

\newline

Jon and Valeria 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, Jon has

28

signatures, and Valeria has

10

. Jon is collecting signatures at an average rate of

6

per day, whereas Valeria is averaging

15

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, Jon and Valeria will each have collected

\_

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

\newline

Omar, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for

\$5

, and paint and canvas for each painting costs

\$67

; he will sell each painting for

\$68

. Once Omar sells a certain number of his paintings, he will be breaking even. How much will Omar have earned? How many paintings will that be?

\newline

Omar's expenses and receipts will both total

\$\_\_\_\_

when he has sold

\_\_\_

of his paintings.

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

\newline

Mrs. Hutchinson is a dance teacher whose students are going to have a recital. She is comparing two companies' prices for filming the recital and producing DVDs. Kevin's Productions charges

\$3

\$99

to come and film the recital. Somerville Media charges

\$54

\$4

per DVD. To decide which company to use, Mrs. Hutchinson determines the number of DVDs that would make the two options equivalent in terms of cost. How much would each option cost? How many DVDs would that be?

\newline

The cost would be

\$

_____ if Mrs. Hutchinson ordered _____ DVDs.

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

\newline

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

1

page per minute, while Eve can read

2

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

40

pages, and Eve had already gotten through

39

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

\newline

Ronald and Eve had each read

\_

\_

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

\newline

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

\$16

to ship a medium box, plus an additional

\$6

per kilogram. A second shipping company charges

\$12

for the same size of box, plus an additional

\$8

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

\newline

The two shipping methods both cost

\$

_____ at a weight of _____ kilograms.

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

\newline

A company that teaches self-improvement seminars is holding one of its seminars in Campbell. The company pays a flat fee of

\$208

to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend

\$2

to purchase books and supplies. Each attendee will pay

\$15

for the seminar. Once a certain number of attendee register, the company will be breaking even. How many attendees will that take? What will be the company's total expenses and revenues?

\newline

\_\_

attendees have registered, the company's expenses and receipts will both total

\$\_\_

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

\newline

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

4\,\text{meters per second}

, and Camille can run

5\,\text{meters per second}

. Mrs. Landry decides to give Patrick a head start of

26\,\text{meters}

since he runs more slowly. Once the students start running, Camille will quickly catch up to Patrick. How long will that take? How far will Camille have to run?

\newline

\_\_\_

seconds for Camille to run

\_\_\_

meters and catch up to Patrick.

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

\newline

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

\$201

for showing up, plus

\$71

per hour. Cindy charges

\$198

\$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 duration be? What would the cost be?

\newline

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

\$

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

\newline

Mrs. Sloan is a dance teacher whose students are going to have a recital. She is comparing two companies' prices for filming the recital and producing DVDs. Joy's Productions charges

\$4

\$70

to come and film the recital. Lanberry Media charges

\$79

\$3

per DVD. To decide which company to use, Mrs. Sloan determines the number of DVDs that would make the two options equivalent in terms of cost. How many DVDs would that be? How much would each option cost?

\newline

If Mrs. Sloan ordered _____ DVDs, the cost would be

\$

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

\newline

Sanjay, a caterer, is investing some money in equipment and employees to help grow his business. Recently he spent

\$98

on equipment and hired a server who makes

\$13

per hour. Sanjay is hoping to make up these expense at the next job that is scheduled, which pays a base of

\$95

\$14

per hour that the server works. In theory, this event could pay enough to cancel out Sanjay's expenditures. How long would the job have to be? How much would the job pay?

\newline

If the job lasted _____ hours, the expenditures and pay would both be

\$

Solve the system of equations.

-9x + 4y = 6

9x + 5y = -33

The ratio of new car sales to used car sales at the car lot is

3:5

. If the total car sales were

\$287,400

last month, what was the total of the used car sales?

A building contractor has a pickup truck with a rear storage area in the shape of a rectangular prism. The storage area has a length of

80

inches (in), a width of

60

\mathrm{in}

, and a height of

44

\mathrm{in}

. She wants to fill the entire storage area with equal-sized rectangular prism-shaped bricks with lengths of

8

\mathrm{in}

4

\mathrm{in}

, and heights of

2

\mathrm{in}

. How many bricks can the contractor fit in the storage area of her truck?