Test bank and solution algebra solving equations and problems (1)

The correct choice is c.. Chapter 11 Mid-Chapter Review 1... Chapter 11 Summary and Review: Review Exercises 219Chapter 11 Concept Reinforcement 1.. Chapter 11 Review Exercises... Chapte

a +
9

5− 310



b − 42

=
39

6 − 46



a +
18

10− 310

Exercise Set 11.2

RC2 To solve the equation 3 + x = −15, we would first

subtract 3 on both sides The correct choice is (c)

RC4 To solve the equation x + 4 = 3, we would first add −4

on both sides The correct choice is (a)

12 = x

48 12318

RC2 To solve the equation −6x = 12, we would first divide

by −6 on both sides The correct choice is (d).RC4 To solve the equation 1

6x = 12, we would first multiply

by 6 on both sides The correct choice is (b)

Chapter 11 Mid-Chapter Review 213

56 To “undo” the last step, divide 22.5 by 0.3

22.5 ÷ 0.3 = 75Now divide 75 by 0.3

75 ÷ 0.3 = 250The answershould be 250 not 22.5

Chapter 11 Mid-Chapter Review

1 False; 2(x + 3) = 2 · x + 2 · 3, or2x + 6 = 2 · x + 3

2 True; see page 629 in the text

3 True; see page 630 in the text

x + 9 − 9 = −3 − 9

x = −12The solution is −12

y − 7 + 7 = −2 + 7

y = 5The solution is 5

3 + t − 3 = 10 − 3

t = 7The solution is 7

−5 + x + 5 = 5 + 5

x = 10The solution is 10

y = −56The solution is −56

4.

4.6 − 3.9 = x + 3.9 − 3.90.7 = x

The solution is 0.7

−3.3 + 1.9 = −1.9 + t + 1.9

−1.4 = tThe solution is −1.4

38 7x = 427x

427

x = 6The solution is 6

39 144 = 12y144

12 =

12y12

12 = yThe solution is 12

−1 · 17 = −1(−t)

−17 = tThe solution is −17

41 6x = −546x

−546

x = −9The solution is −9

t = 53The solution is5

50 They are not equivalent For example, let a = 2 and b = 3.Then (a+b)2

52 The student probably added1

3 on both sides of the tion rather than adding −13 (orsubtracting 1

equa-3) on bothsides The correct solution is −2

53 The student apparently multiplied by −2

3 on both sidesrather than dividing by 2

3 on both sides The correct lution is −52

so-Exercise Set 11.4

RC2 The correct choice is (a)

RC4 The correct choice is (e)

2 8x + 6 = 308x = 24

x = 3

4 8z + 7 = 798z = 72

26x − 4 = 1 + 16x

10x = 5

x =12

48 −32+ x = −56−43, LCM is 6

−9 + 6x = −5 − 8

−9 + 6x = −136x = −4

y = 125

75 =

53

56 1.7t + 8 − 1.62t = 0.4t − 0.32 + 8170t + 800 − 162t = 40t − 32 + 800

11y = 32 + 4y7y = 32

y = 327

60 4(2y − 3) = 288y − 12 = 288y = 40

m = 9

66 6b − (3b + 8) = 166b − 3b − 8 = 163b − 8 = 163b = 24

b = 8

x = 3914

x = −325

Exercise Set 11.5

RC2 Translate to an equation

RC4 Check yourpossible answerin the original problem

2 Let x = the number; 3x

a .

4 Let b = the number; 43%b, or 0.43b

6 Let n = the number; 8n − 75

8 Solve: 8n = 2552

n = 319The numberis 319

10 Let c = the numberof calories in a cup of whole milk.Solve: c − 89 = 60

c = 149 calories

12 Solve: 5x − 36 = 374

x = 82The numberis 82

14 Solve: 2y + 85 = 3

4y

y = −68The original number is −68

16 Let h = the height of the control tower at the Memphisairport, in feet

Solve: h + 59 = 385

h = 326 ft

18 Solve: 84.95 + 0.60m = 250

m = 275.083Molly can drive 275 mi

218Chapter 11: Algebra: Solving Equations and Problems

20 Let p = the price of one shirt Then 2p = the price of

anothershirt

Solve: p + 2p + 27

p = $25, so 2p = 2 · $25 = $50 The prices of the other two

shirts are $25 and $50

22 Let w = the width of the two-by-four, in inches

Solve: 2(2w + 2) + 2w = 10

w = 3

2, or1

12

If w = 11

2, then w + 2 = 3

1

2.The length is 31

2 in and the width is 1

30 We draw a picture We let x = the measure of the first

angle Then 4x = the measure of the second angle, and

(x + 4x) − 45, or5x − 45 = the measure of the third angle

x

2nd angle4x

3rd angle5x − 45

Solve: x + 4x + (5x − 45) = 180

x = 22.5, 4x = (22.5) = 90, and 5x − 45 = 5(22.5) − 45 =

67.5, so the measures of the first, second, and third angles

are 22.5◦, 90◦, and 67.5◦, respectively

32 Let m = the numberof miles a passengercan travel for

54 Solve: 2 · 85 + s

s = 76The score on the third test was 76

Chapter 11 VocabularyReinforcement

1 When we replace a variable with a number, we say that

we are substituting forthe variable

2 A letterthat stands forjust one numberis called aconstant

3 The identity property of 1 states that forany real number

Chapter 11 Summary and Review: Review Exercises 219

Chapter 11 Concept Reinforcement

1 True; for instance, when x = 1, we have x−7 = 1−7 = −6

but 7 − x = 7 − 1 = 6 The expressions are not equivalent

2 False; the variable is not raised to the same power in both

terms, so they are not like terms

x + 5 − 5 = 2 − 5

x = −3Since x = −3 and x = 3 are not equivalent, we know

that x + 5 = 2 and x = 3 are not equivalent The given

9x

−729

5 =

55

y = 1The solution is 1

8 6x − 4 − x = 2x − 10

5x − 4 = 2x − 105x − 4 − 2x = 2x − 10 − 2x3x − 4 = −10

3x − 4 + 4 = −10 + 43x = −63x

3 =

−63

x = −2The solution is −2

9 2(y − 1) = 5(y − 4)

2y − 2 = 5y − 202y − 2 − 5y = 5y − 20 − 5y

10 Let n = the number We have n + 5, or 5 + n

Chapter 11 Review Exercises

n − 7 + 7 = −6 + 7

n = 1The number1 checks It is the solution

18 15x = −35

15x

15 =

−3515

2 checks It is the solution.

5y = −1635

y − 0.9 + 0.9 = 9.09 + 0.9

y = 9.99The number9.99 checks It is the solution

24 5t + 9 = 3t − 15t + 9 − 3t = 3t − 1 − 3t2t + 9 = −12t + 9 − 9 = −1 − 92t = −102t

2 =

−102

t = −5The number −5 checks It is the solution

−13= xThe number −13 checks It is the solution

4x −58= 3

81

4x =

881

4x = 1

4 ·14x = 4 · 1

x = 4The number4 checks It is the solution

Chapter 11 Summary and Review: Review Exercises 221

28 0.22y − 0.6 = 0.12y + 3 − 0.8y

0.22y − 0.6 = −0.68y + 30.22y − 0.6 + 0.68y = −0.68y + 3 + 0.68y

0.9y − 0.6 = 30.9y − 0.6 + 0.6 = 3 + 0.6

0.9y = 3.60.9y0.9 =

3.60.9

y = 4The number4 checks It is the solution

8x +

1

16x = 3 −161x + 1

16x2

16x +

1

16x = 33

16x = 316

30 4(x + 3) = 36

4x + 12 = 36

4x + 12 − 12 = 36 − 12

4x = 244x

4 =

244

x = 6The number6 checks It is the solution

31 3(5x − 7) = −66

15x − 21 = −6615x − 21 + 21 = −66 + 21

15x = −4515x

15 =

−4515

x = −3The number −3 checks It is the solution

32 8(x − 2) − 5(x + 4) = 20x + x8x − 16 − 5x − 20 = 21x

3x − 36 = 21x3x − 36 − 3x = 21x − 3x

−36 = 18x

−36

18 =

18x18

−2 = xThe number −2 checks It is the solution

34 Let x = the number; 19%x, or 0.19x

35 Familiarize Let w = the width Then w + 90 = thelength

Translate We use the formula for the perimeter of arectangle, P = 2 · l + 2 · w

1280 = 2 · (w + 90) + 2 · wSolve

1280 mi The answerchecks

State The length is 365 mi, and the width is 275 mi

36 Familiarize Let l = the length of the shorter piece, in ft.Then l + 5 = the length of the longerpiece

Translate.Length ofshorter piece

plus length oflongerpiece

is Totallength

  

l = 8

If l = 8, then l + 5 = 8 + 5 = 13

Check A 13-ft piece is 5 ft longerthan an 8-ft piece and

the sum of the length is 8 ft + 13 ft, or21 ft The answer

checks

State The lengths of the pieces are 8 ft and 13 ft

37 Familiarize Let p = the price of the mower in February

answerchecks

State The price of the mower in February was $2117

38 Familiarize Let a = the numberof appliances Ty sold

Translate

Commission

Commissionforeachappliance

times

Numberofappliancessold

Check 27 · $8 = $216, so the answerchecks

State Ty sold 27 appliances

39 Familiarize Let x = the measure of the first angle Then

x + 50 = the measure of the second angle and 2x − 10 =

the measure of the third angle

Translate The sum of the measures of the angles of a

State The measure of the first angle is 35◦, the measure

of the second angle is 85◦, and the measure of the thirdangle is 60◦

40 Familiarize Let p = the marked price of the breadmaker

Translate.Markedprice

p = 220Check 30% of $220 = 0.3 · $220 = $66 and

$220 − $66 = $154 The answerchecks

State The marked price of the bread maker was $220

41 Familiarize Let a = the amount the organization ally owes This is the cost of the office supplies withoutsales tax added

actu-Translate.Amountowed

a ≈ 138.95Check 5% of $138.95 = 0.05 · $138.95 ≈ $6.95 and

$138.95 + $6.95 = $145.90 The answerchecks

State The organization actually owes $138.95

42 Familiarize Let s = the previous salary

Translate.Previoussalary

s = 68, 000Check 5% of $68, 000 = 0.05 · $68, 000 = $3400 and

$68, 000 + $3400 = $71, 400 The answerchecks

State The previous salary was $68,000

the cost of the television in May, so the answerchecks.

State The television cost $867 in January

44 Familiarize Let l = the length Then l − 6 = the width

Translate We use the formula for the perimeter of a

State The length is 17 cm, and the width is 11 cm

45 Familiarize The Nile Riveris 234 km longerthan the

Amazon River, so we let l = the length of the Amazon

Riverand l + 234 = the length of the Nile River

is Totallength

l = 6437

If l = 6437, then l + 234 = 6437 + 234 = 6671

Check 6671 km is 234 km more than 6437 km, and

6671 km + 6437 km = 13, 108 km The answerchecks

State The length of the Amazon Riveris 6437 km, and

the length of the Nile Riveris 6671 km

48 2|n| + 4 = 50

2|n| = 46

|n| = 23The solutions are the numbers whose distance from 0 is

23 Thus, n = −23 or n = 23 These are the solutions

49 |3n| = 603n is 60 units from 0, so we have:

3n = −60 or 3n = 60

n = −20 or n = 20The solutions are −20 and 20

Chapter 11 Discussion and Writing Exercises

1 The distributive laws are used to multiply, factor, and lect like terms in this chapter

col-2 Foran equation x + a = b, we add the opposite of a onboth sides of the equation to get x alone

3 Foran equation ax = b, we multiply by the reciprocal of

a on both sides of the equation to get x alone

4 Add −b (orsubtract b) on both sides and simplify Thenmultiply by the reciprocal of c (ordivide by c) on bothsides and simplify

2x −35= 2

51

2x = 1

2 ·12x = 2 · 1

x = 2The answerchecks The solution is 2

16 0.4p + 0.2 = 4.2p − 7.8 − 0.6p

0.4p + 0.2 = 3.6p − 7.8 Collecting like terms

on the right0.4p + 0.2 − 0.4p = 3.6p − 7.8 − 0.4p

0.2 = 3.2p − 7.80.2 + 7.8 = 3.2p − 7.8 + 7.8

8 = 3.2p83.2 =

3.2p3.22.5 = pThe answerchecks The solution is 2.5

17 3(x + 2) = 27

3x + 6 = 27 Multiplying to remove parentheses3x + 6 − 6 = 27 − 6

3x = 213x

213

x = 7The answerchecks The solution is 7

3.

19 Let x = the number; x − 9

Chapter 11 Test 225

20 Familiarize We draw a picture Let w = the width of

the photograph, in cm Then w + 4 = the length

w + 4

w + 4

ww

The perimeter P of a rectangle is given by the formula

2l + 2w = P , where l = the length and w = the width

Translate We substitute w + 4 for l and 36 for P in the

formula for perimeter

2l + 2w = P2(w + 4) + 2w = 36

Solve We solve the equation

2(w + 4) + 2w = 36

2w + 8 + 2w = 36

4w + 8 = 364w = 28

w = 7Possible dimensions are w = 7 cm and w + 4 = 11 cm

Check The length is 4 cm more than the width The

perimeter is 2 · 11 cm + 2 · 7 cm, or36 cm The result

x ≈ 46, 120 Rounding to the nearest tenCheck 17% of $46, 120 = 0.17 · $46, 120 = $7840.4 ≈

$7840, so the answerchecks

State The Ragers’ income was about $46,120

22 Familiarize Using the labels on the drawing in the text,

we let x and x + 2 represent the lengths of the pieces, in

is Length ofthe board

State The pieces are 3 m and 5 m long

23 Familiarize Let t = the tuition U.S universities receivedfrom foreign students in 2005-2006, in billions of dollars.Translate

2005-2006tuition

t = 14.31.52≈ 9.4Check 52% of 9.4 = 0.52 · 9.4 = 4.888, and 9.4 + 4.888 =14.288 ≈ 14.3, so the answerchecks

State U.S universities received about $9.4 billion in ition from foreign students in 2005-2006

tu-24 Familiarize Let n = the original number

Translate.Three times a number

State The original number is 6

25 Familiarize We draw a picture We let x = the measure

of the first angle Then 3x = the measure of the secondangle, and (x + 3x) − 25, or4x − 25 = the measure of thethird angle

x

2nd angle3x

3rd angle4x − 25

Recall that the measures of the angles of any triangle add

up to 180◦

measure ofthird angle is 180◦.

(4x − 25) = 180Solve We solve the equation

x + 3x + (4x − 25) = 180

8x − 25 = 1808x = 205

x = 25.625Although we are asked to find only the measure of the first

angle, we find the measures of the other two angles as well

so that we can check the answer

Possible answers for the angle measures are as follows:

First angle: x = 25.625◦

Second angle: 3x = 3(25.625) = 76.875◦

Third angle: 4x − 25 = 4(25.625) − 25

= 102.5 − 25 = 77.5◦

Check.Consider25.625◦, 76.875◦, and 77.5◦ The second

is three times the first, and the third is 25◦less than four

times the first The sum is 180◦ These numbers check

State.The measure of the first angle is 25.625◦

2 =

82

y = 4The answer checks The solution is 4 Answer D is correct

28 Familiarize Let t = the numberof tickets given away

Then the first person got1

3t tickets, the second person got1

4t, the third person got

13· 13 = 60

13·13

60t

60 = tCheck 1

3· 60 = 20, 14· 60 = 15, and 15· 60 = 12 Since

20 + 15 + 12 + 8 + 5 = 60, the answerchecks

State 60 tickets were given away

Cumulative Review Chapters 1 - 11

1 47,201The digit 7 tells the numberof thousands

2 7405 = 7 thousands + 4 hundreds + 0 tens + 5 ones, or

7 thousands + 4 hundreds + 5 ones

3 7.463a) Write a word name for

c) Write a word name forthe numberto the right Seven

followed by the placevalue of the last digit

fourhundredsixty-threethousandths

A word name for7.463 is seven and fourhundred three thousandths

sixty-4

1

7 4 1+ 2 7 1

1 0 1 25

2 1 1

4 9 0 3

5 2 7 8

6 3 9 1+ 4 5 1 3

26

Cumulative Review Chapters 1 - 11 227

49+3 1

3·33 = +33

9

5798

−1 5

8·33 = −11524 = −11524

21724

5 = 3

3525

27 A mixed numeral for the quotient in Exercise 26 is:

29 2 ÷ 30 = 73÷ 30 = 73·301 = 7

90

228Chapter 11: Algebra: Solving Equations and Problems

31 6 8, 4 8 9

↑

The digit 8 is in the thousands place Considerthe next

digit to the right Since the digit, 4, is 4 or lower round

down, meaning that 8 thousands stay as 8 thousands

Then change all digits to the right of the thousands digit

2 1 8 3 8 3 to the nearest hundredth

↑ Thousandths digit is 5 orhigher

↓

34 A numberis divisible by 6 if it is even and the sum of its

digits is divisible by 3 The number1368 is even The sum

of its digits, 1 + 3 + 6 + 8, or 18, is divisible by 3, so 1368

37 We multiply these We multiply these

5 =

3

5·77= 21

35Since 20 < 21, it follows that 20

1.001

↑ Different; 1 is larger than 0.

↓0.9976Thus, 1.001 is larger

40 $0.95

8 oz

= 95/c8.5 oz ≈ 11.176/c/ oz

41 a) C = π · d

C ≈ 227 · 1400 mi = 4400 mib) First we find the radius

43 Let p = the percent of the cost represented by the tertops

Cumulative Review Chapters 1 - 11 229

44 Let a = the cost of the appliances

The appliances cost $3495.44

45 Let p = the percent of the cost represented by the fixtures

46 Let f = the cost of the flooring

47 Since 987 is to the right of 879 on the number line, we have

987 > 879

48 The rectangle is divided into 5 equal parts The unit is1

5.The denominatoris 5 We have 3 parts shaded This tells

us that the numerator is 3 Thus, 3

9= 0.888 , or0.8.

52 7%

a) Replace the percent symbol with ×0.01

7 × 0.01b) Move the decimal point two places to the left

0 07

↑Thus, 7% = 0.07

↑

463100

2 places Move 2 places 2 zeros4.63 =463

↑b) Write a percent symbol: 150%

Thus, 1.5 = 150%

234 + y − 234 = 789 − 234

y = 555The number555 checks It is the solution