A Park Ranger’s Work Is Never Donerobertsk.weebly.com/uploads/2/4/9/7/24972307/carnegie...Chapter 1 Skills Practice • 315 © 2011 Carnegie Learning A Park Ranger’s Work Is Never

Chapter 1 Skills Practice • 315

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A Park Ranger’s Work Is Never DoneSolving Problems Using Equations

VocabularyGive an example of each term.

1. two-step equation

2. inverse operations

3. solution

4. coefficient

5. constant

6. Properties of Equality

Problem SetName the inverse operations at each step.

1. 5x 1 15 5 75

5x 1 15 2 15 5 75 2 15 Add 15 and subtract 15.

5x 5 60

5x ___ 5

5 60 ___ 5

Multiply by 5 and divide by 5.

x 5 12

Lesson 1.1 Skills Practice

Name ________________________________________________________ Date _________________________

316 • Chapter 1 Skills Practice

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Lesson 1.1 Skills Practice page 2

2. 4x 2 3 5 37

4x 2 3 1 3 5 37 1 3

4x 5 40

4x ___ 4

5 40 ___ 4

x 5 10

3. t __ 3 1 14 5 29

t __ 3 1 14 2 14 5 29 2 14

t __ 3

5 15

3 ( t __ 3

) 5 3(15)

t 5 45

4. z __ 9 2 4 5 7

z __ 9 2 4 1 4 5 7 1 4

z __ 9

5 11

9 ( z __ 9 ) 5 9(11)

z 5 99


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Name ________________________________________________________ Date _________________________

5. 11 1 3x 5 38

11 2 11 1 3x 5 38 2 11

3x 5 27

3x ___ 3 5 27 ___

3

x 5 9

6. 8x 2 12 5 20

8x 2 12 1 12 5 20 1 12

8x 5 32

8x ___ 8

5 32 ___ 8

x 5 4

7. 31 1 x __ 7

5 150

31 2 31 1 x __ 7

5 150 2 31

x __ 7

5 119

7 ( x __ 7 ) 5 7(119)

x 5 833


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8. 52 2 m ___ 11

5 40

52 2 52 2 m ___ 11

5 40 2 52

2 m ___ 11 5 212

211 ( 2 m ___ 11 ) 5 211(212)

m 5 132

Solve each equation. Name the inverse operations at each step.

9. 12x 1 7 5 67

12x 1 7 2 7 5 67 2 7 Add 7 and subtract 7.

12x 5 60

12x ____ 12

5 60 ___ 12

Multiply by 12 and divide by 12.

                  x 5 5

10. 6x 2 9 5 33


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Name ________________________________________________________ Date _________________________

11. 6 1 m ___ 12

5 18

12. t ___ 10

2 21 5 2161

13. 5.4x 1 13 5 121


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14. 22.8 2 2p 5 44.4

15. 3 __ 4 g 116 5 34

16. x ___ 12

2 5 5 3.75


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Name ________________________________________________________ Date _________________________

Solve each equation.

17. 10x 1 13 5 150

10x 1 13 5 150

10x 1 13 2 13 5 150 2 13

10x 5 137

10x ____ 10

5 137 ____ 10

x 5 13.7

19. 85 1 c __ 4

5 99

18. 6t 2 10 5 86

20. 9.6m 1 6 5 30


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21. 25 2 z __ 8 5 12.5

23. 220 5 55 2 5.5w

22. 3t 2 1 __ 4 5 7 __ 8

24. 3 __ 5

x 2 3 5 2 1 __ 4

7721B_C3_Skills_CH01_315-354.indd 322 11/03/14 9:53 AM


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25. 25.2t 2 14.5 5 300.5 26. z ___ 30

1 275 5 1225


Name ________________________________________________________ Date _________________________


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Why Doesn’t This Work?Equations with Infinite or No Solutions

Problem SetComplete each table to determine whether the given equation has no solutions or an infinite number

of solutions.

1. 6x 210 5 3x 1 5 1 3(x 2 5)

x 6x 2 10 3x 1 5 1 3(x 2 5)

22 6(22) 210 5 212 210 5 2223(22) 1 5 1 3(22 2 5) 5 26 1 5 1 3(27) 5

211 (221) 5 222

0 6(0) 210 5 0 210 5 2103(0) 1 5 1 3(0 2 5) 5 0 1 5 1 3(25) 5

5 1 (215) 5 210

4 6(4) 210 5 24 210 5 143(4) 1 5 1 3(4 2 5) 5 12 1 5 1 3(21) 5

17 1 (23) 5 14

The equation has an infinite number of solutions.

2. 2x 1 5 1 3x 2 3 5 5x 1 9

x 2x 1 5 1 3x 2 3 5x 1 9

21

1

5


Name ________________________________________________________ Date _________________________


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3. 2(4x 1 3) 5 2x 1 6 1 3(2x)

x 2(4x 1 3) 2x 1 6 1 3(2x)

1

3

6

4. 9x 1 5 5 12x 1 3(7 2 x)

x 9x 1 5 12x 1 3(7 2 x)

25

2

7

5. 8x 2 8 5 6x 2 5 1 2(x 2 2)

x 8x 2 8 6x 2 5 1 2(x 2 2)

23

1

8


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6. 5(2 2 x) 5 2x 1 7 2 7x 1 3

x 5(2 2 x) 2x 1 7 2 7x 1 3

22

0

2

Solve each equation and determine whether the equation has no solutions, one solution, or an infinite

number of solutions.

7. 4(2x 1 1) 2 3(x 2 2) 5 10 1 5x

4(2x 1 1) 2 3(x 2 2) 5 10 1 5x

8x 1 4 2 3x 1 6 5 10 1 5x

8x 2 3x 1 4 1 6 5 10 1 5x

5x 1 10 5 10 1 5x

5x 2 5x 1 10 5 10 1 5x 2 5x

10 5 10

The equation has an infinite number of solutions.


Name ________________________________________________________ Date _________________________

7721B_C3_Skills_CH01_315-354.indd 327 08/03/14 11:51 AM


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8. 10(x 2 2) 1 15 5 8x 1 7


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Name ________________________________________________________ Date _________________________

9. x 1 6(x 2 1) 5 7(3 1 x)

10. 12x 1 9 2 4x 2 4 5 3x 2 7 2 x 1 30


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11. 3(3x 1 4) 2 2x 2 5 2 7x 5 20

12. 5(4x 2 2) 1 9 5 2(8x 1 7)


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Name ________________________________________________________ Date _________________________

13. 4x 1 1 1 3x 1 2 1 2x 1 3 1 x 1 4 5 5(2x 1 2)

14. 29x 1 12 1 4(3x 2 3) 5 7(x 2 2) 2 4x 1 14


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15. 7 2 2(25x 2 9) 1 2x 5 4(2x 2 1) 1 3(x 1 12)


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Name ________________________________________________________ Date _________________________

16. 2.5x 1 15 1 0.5(x 2 4) 5 1.2x 1 2(0.9x 2 6)


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Who Has The Most?Solving Linear Equations

Problem SetDefine a variable and write algebraic expressions for each of the given quantities. Then, answer the

question by writing and solving an equation.

1. The middle school dance team had 3 separate car washes on Saturday to raise money for new

uniforms. The Main Street location raised $50 more than the Back Street location. The Washington

Street location raised $50 more than half the amount raised at the Back Street location. How much

did the dance team raise at each location if they raised a total of $600?

Let x represent the amount of money raised at the Back Street location.

Amount of money raised at the Main Street location: x 1 50

Amount of money raised at the Washington Street location: 0.5x 1 50

x 1 x 1 50 1 0.5x 1 50 5 600

2.5x 1 100 5 600

2.5x 1 100 2 100 5 600 2 100

2.5x 5 500

2.5x ____ 2.5

5 500 _____ 2.5

x 5 200

Amount of money raised at the Main Street location: 200 1 50 5 250

Amount of money raised at the Washington Street location: 0.5(200) 1 50 5 150

The dance team raised $200 at the Back Street location, $250 at the Main Street location, and

$150 at the Washington Street location.


Name ________________________________________________________ Date _________________________


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2. Three brothers spent different amounts of money on their recent vacation. Matt spent $25 less

than Todd. Jeff spent 3 times as much as Matt. How much did each brother spend if they spent a

total of $275?


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Name ________________________________________________________ Date _________________________

3. Three waiters at a local restaurant earned different amounts of money the past week. Jennifer

earned $40 less than twice the amount Tony earned. Chris earned $60 more than Tony. How much

did each waiter earn if they earned a total of $900?


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4. Four friends have different numbers of cows on their farms. Jorge has 3 times as many cows as

Carla. Marcus has half as many cows as Jorge. Dominique has 2 less than 4 times as many cows

as Carla. How many cows does each person have if they have a total of 169 cows?


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Name ________________________________________________________ Date _________________________

5. Tommy gives baseball cards to four of his friends. He gives Kiana 3 cards less than he gives Gary.

He gives Monty 7 cards more than he gives Kiana. He gives Willa twice as many as he gives

Monty. How many cards does Tommy give to each friend if he gives out a total of 74 cards?


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6. Terry types twice as many words per minute as Cecilia. Paige types 5 words per minute less than

Terry. Reggie types 10 words per minute more than Terry. How many words per minute does each

person type if the total number of words per minute that Reggie and Cecilia type equals the total

number of words per minute that Terry and Paige type?


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Name ________________________________________________________ Date _________________________

7. Four friends are collecting canned goods for charity. Ron collects 10 more than 3 times as many

cans as Jasmine. Barry collects twice as many cans as Jasmine. Alicia collects 10 more cans than

Barry. How many cans does each person collect if Jasmine and Ron collect the same number of

cans as Alicia and Barry?


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8. At an archery competition, Jamie and Marshall’s team tied Shawna and Wyatt’s team for the top

team score. Team scores are determined by adding the two team member’s individual scores.

Marshall scored 12 less than Jamie. Shawna scored twice as much as Marshall. Wyatt scored

4 less than Shawna. What was each person’s individual score?


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Name ________________________________________________________ Date _________________________

9. Four employees at a crayon factory are working on four separate machines. Cynthia’s machine

produces 100 less than twice the number of crayons as Zane’s machine every hour. Louisa’s

machine produces 50 crayons more than Zane’s machine every hour. Evan’s machine produces

20 crayons less than Cynthia’s machine every hour. How many crayons must Zane’s machine

produce every hour in order for Cynthia and Zane’s output to equal Louisa and Evan’s output?


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10. Four employees are cleaning out four different wishing wells at an amusement park. Tracy

collects $5.80 more than Asuka. Kyle collects half as much as Tracy. Beverly collects 3 times

as much as Kyle. How much money does each employee collect if the total amount of money

collected is $246.20?


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Games and PracticeSolving More Linear Equations

Problem SetDefine a variable and write algebraic expressions for each of the given quantities. Then, answer the

question by writing and solving an equation.

1. Three siblings collect rare coins. To determine the number of rare coins that Samantha has, take

the number of rare coins Kevin has, add 4, and then divide that sum by 2. To determine

the number of rare coins Ben has, double the amount of rare coins Kevin has, subtract 4, and then

multiply that difference by 2. How many rare coins does each sibling have if they have a total

of 49 rare coins?

Let x represent the number of rare coins that Kevin has. Number of rare coins Samantha has:

(10 1 4)

________ 2

5 7

Number of rare coins Ben has:

2(2(10) 2 4) 5 32

Kevin has 10 rare coins, Samantha

has 7 rare coins, and Ben has

32 rare coins.

Number of rare coins Samantha has: (x 1 4 )

_______ 2

Number of rare coins Ben has: 2(2x 2 4)

  x 1 (x 1 4)

_______ 2

1 2(2x 2 4) 5 49

2 ( x 1 (x 1 4)

_______ 2

1 2(2x 2 4) ) 5 2(49)

2x 1 x 1 4 1 4(2x 2 4) 5 98

3x 1 4 1 8x 2 16 5 98

11x 2 12 5 98

11x 2 12 1 12 5 98 1 12

11x 5 110

11x ____ 11

5 110 ____ 11

   x 5 10


Name ________________________________________________________ Date _________________________


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2. Three teammates had different point totals at the girls’ basketball game. To determine the number

of points Effie had, multiply Toni’s points by 3, subtract 8, and then multiply the difference by 2.

To determine the number of points Linda had, add 9 to Toni’s points and divide the sum by 3.

How many points did each girl have if Effie scored 9 more than Toni and Linda combined?


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Name ________________________________________________________ Date _________________________

3. Four members of the track team ran various numbers of miles last week. To determine the

number of miles Manuel ran, multiply the number of miles Ewan ran by 3, subtract 15, multiply the

difference by 2, and divide this quantity by 5. To determine the number of miles Violet ran,

subtract 14 from the number of miles Ewan ran, and then multiply the difference by 3. To determine

the number of miles Ling ran, add 30 to the number of miles Ewan ran, and then divide the sum

by 5. How many miles did each team member run last week if the total number of miles ran by

Ewan and Manuel is equal to the total number of miles ran by Violet and Ling?


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4. Four friends have pre-paid cell phones. To determine the number of minutes Warren has left on

his phone, add 20 to the number of minutes Nancy has and divide the sum by 4. To determine the

number of minutes Christen has left on her phone, multiply the number of minutes Nancy has by

3, subtract 50, and then divide the difference by 2. To determine the number of minutes Megan has

left on her phone, subtract 20 from the number of minutes Nancy has, multiply the difference by

5, and then divide that quantity by 4. How many minutes does each person have left on their

phone if they have a total of 195 minutes of time left?


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Name ________________________________________________________ Date _________________________

Solve each equation. Check your solution.

5. 4(x 2 8)

________ 5 5 16

4(x 2 8)

________ 5 5 16 Check:

5 ( 4(x 2 8) ________

5 ) 5 5(16)

4(28 2 8) _________

5 5 16

4(x 2 8) 5 80 4(20)

_____ 5

5 16

4x 2 32 5 80 80 ___ 5 5 16

4x 2 32 1 32 5 80 1 32 16 5 16

4x 5 112

4x ___ 4

5 112 ____ 4

x 5 28

6. 3x 1 5 _______ 4

5 2x 2 2 _______ 2


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7. 5(x 2 4) 1 8(2x 1 2) 5 6(x 1 1) 1 5(x 1 10)


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Name ________________________________________________________ Date _________________________

8. 25(x 2 2)

_________ 2

5 2 2 8x _______ 6


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9. 2(x 1 3)

________ 3 1 7 __

3 5 5(x 2 12) 2 2 __

3


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Name ________________________________________________________ Date _________________________

10. 23x 1 3 ________ 5 1 1 __

5 5

2(4 2 x) ________

5


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Documents

A Park Ranger’s Work Is Never Donerobertsk.weebly.com/uploads/2/4/9/7/24972307/carnegie...Chapter 1 Skills Practice • 315 © 2011 Carnegie Learning A Park Ranger’s Work Is Never