Resources

Resources

Solve a system of equations using substitution: word problems

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

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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?

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\_\_\_

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.

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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?

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\_

hours, both men will have completed

\_

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

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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?

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\_

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?

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470

seats for general admission and

525

seats for lower level

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290

seats for general admission and

705

seats for lower level

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565

seats for general admission and

430

seats for lower level

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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

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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?

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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.

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The ratio of blue pencils to purple pencils is

14: 9

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The ratio of purple pencils to pink pencils is

1: 3

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Calculate the percentage of pencils that are pink.

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Variability describes how much the data values in a data set differ, or vary, from each other.

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high variability

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Label each data display to describe its level of variability.

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Which race was more competitive, this year's or last year's?

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Last Year's Car Race

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A coffee shop wants to serve coffee at the same temperature every time for the best taste. On average, both shop workers hit the shop goal. However, the shop manager thinks one worker does a better jc than the other.

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Tell what temperature the shop wants the coffee to be. Then explair who the manager thinks did a better job.

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Coffee Temperature by Cup (

{ }^{\circ} \mathrm{F}

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\begin{tabular}{|l|l|l|l|l|l|l|l|}

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\hline Worker A &

155

160

150

145

170

175

165

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\hline Worker B &

155

160

163

157

162

158

165

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

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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?

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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.

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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?

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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. 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.

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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?

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Each burrito platter costs

\$\_\_\_\_

and each taco platter costs

\$\_\_\_\_

3

. Tom and Rob are brothers who like to make bets about the outcomes of different contests between them. Before the last bet, the ratio of the amount of Tom's money to the amount of Rob's money was

4: 7

. Rob lost the latest competition, and now the ratio of the amount of Tom's money to the amount of Rob's money is

8: 3

\$ 280

before the last competition, how much does Rob have now that he lost the bet?

Stats Module: Linear Regression/Making Predictions ASSIGNMENT Objective: I can use scatter plots to analyze and make predictions with the data.

1

) The table shows data for cost of airfare vs the distance traveled. Destination: Atlanta Boston Chicago Dallas Detroit Denver Miami New Orleans New York Orlando Pittsburgh St. Louis Distance: Atlanta-

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576

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370

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612

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1216

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409

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1502

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946

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998

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189

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787

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370

0

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370

1

Airfare: Atlanta-

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370

2

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370

3

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370

4

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370

5

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370

6

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370

7

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370

8

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370

9

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612

0

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612

1

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370

3

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612

0

Answer the following questions using a calculator: a) Correlation from graph? Correlation coefficient from calculator? b) Line of Best Fit/Regression Line? c) Based on the regression line, what is the airfare for the destination that is

370

miles away? d) Based on the regression line, what is the airfare for the destination that is

1502

miles away? e) Based on the regression line, a fare of

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612

6

would reach a city of approximately of what distance? f) What airfare would the regression line predict to San Francisco, which is

612

7

miles away. Why might this prediction be less accurate than others?

Concert tickets are sold

£

\$ 100

\$ 60

each, and the revenue from the sale of these tickets is the same as if all tickets were sold at

\$ 90

. What is the ratio of the number of

\$ 100

tickets sold to the number of

\$ 60

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

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

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?

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Getting Ready for High-Stakes

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3

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36

. 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.

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1

5

hours at an average speed of

45

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2

8

hours at an average speed of

35

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The average speed on the third day is

45

miles per hour.

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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.

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Enter your answer and explanation in the space provided. Support your answer using words, numbers, and/or symbols.

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

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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?

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If the Tigers have shirts made, the cost is

\$ \square

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

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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?

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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.

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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?

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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.

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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?

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\_

hours, both men will have completed

\_

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

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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?

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The two trees will both be

\_

\_

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

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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?

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\_

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.

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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?

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\_

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.

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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?

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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.

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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?

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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.

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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?

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\_

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.

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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?

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\_

hours, both men will have completed

\_

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

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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?

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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.

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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?

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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.

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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?

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Ronald and Eve had each read

\_

\_

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

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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?

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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.

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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?

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\_\_

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.

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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?

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\_\_\_

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.

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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?

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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 substitution, and fill in the blanks.

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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?

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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.

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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?

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

\$

Each big square below represents one whole. An array with

10

10

rows that represents

1

10

10

are shaded. An array with

10

10

rows that represents

1

10

10

are shaded. An array with

10

10

rows that represents

1

1

10

1

10

6

is shaded. An array with

10

10

rows that represents

1

1

10

1

10

6

is shaded. What percent is represented by the shaded area?

c. Orange to total marbles

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d. Orange, green and red to orange

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5:15

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8,2:8:5

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Alexis is sharing Lifesavers candy. He is getting rid of all the grapes and keeping the cherry. His ratio from grape to cherry is

15

18

. If Alexis keeps the same ratio and gives his friend

5

grapes how many cherries should he share?

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5

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15

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18

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Alexis Should Share

6

cherries with his friend

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5\times1.2=6

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?

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

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Steven and his cousin Carly are picking apples in their grandparents' orchard. Steven has filled

15

baskets with apples and is filling them at a rate of

4

baskets per hour. Carly has

11

full baskets and will continue picking at

8

baskets per hour. Once the cousins get to the point where they have filled the same number of baskets, they will carry them to the barn and then eat lunch. How long will that take? How much fruit will they have picked by then?

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\_\_\_

hours, the cousins will each have filled

\_\_\_

baskets with apples.