1.1

The pieces are 5 and 15 in.

1.2

The pieces are 3, 4, and 5 ft.

1.3

The pieces are 3 and 6 ft.

1.4

The pieces are called x, 2x, and 2x + 10.

They are 14, 28, and 38 in.

1.5

x + x + 50%x = 275

The ropes are 110 and 165 yards.

1.6

Elsa is 14 years old and Thor is 21 years old.

1.7

The grandmother is 84 years old.

1.8

If Jessica is x, the mother is x + 28, and the grandmother 2(x + 28)

x + x + 28 + 2(x + 28) = 100

x = 4

The grandmother is 2(4 + 28) = 64 years old.

1.9

Answer: Eric is 39 years old and Lucas is 26 years old.

1.10

Michael is 12 years old.

1.11

The number is 26.

1.12

The sun rose at 7:48 a.m.

1.13

The water level was 67.2 ft.

1.14

The population was 503.

1.15

Joan weighed 133 lbs.

1.16

– 6 > – 10

1.17

x ≥ 18

1.18

x ≥ 8

1.19

7, 9, 11, 13, 15

1.20

– 6, – 4, –2

1.21

– 2, – 1, 0, 1, 2

1.22

The first integer is 10.

1.23

The product of 6 and 8 is 48.

1.24

Call the integers x, x + 2, and x + 4

6 x = 5 (x + 2)

x = 10

The largest integer is 14

1.25

The integers are 45, 46, 47, and 48.

1.26

Call the integers x, x + 2, x + 4.

3x = x + 2 + x + 4

The integers are 6, 8, and 10.

1.27

The first odd integer is 7.

1.28

The even integers are 4, 6, and 8.

1.29

Call the integers x and x + 1

The consecutive positive integers are 4 and 5.

1.30

x(x + 4) = 5

The numbers are –5 and –1 or 1 and 5.

1.31

The integers are –5 and –3 or 3 and 5.

1.32

The numbers are 9 and 27 or –9 and –27.

1.33

The numbers are –22 and –20 or 20 and 22.

2.1

1/300

2.2

9/200 or 0.045

2.3

0.00006

2.4

0.017

2.5

4

2.6

300

2.7

0.1875

2.8

525

2.9

0.4

2.10

12%

2.11

0.56%

2.12

1200%

2.13

80%

2.14

66 2/3% or 66.67%

2.15

50,000%

2.16

25%

2.17

6350

2.18

1050

2.19

80%

2.20

$700

2.21

$120

2.22

350

2.23

$80

2.24

$3000

2.25

$11.50

2.26

2.88%

2.27

50%

2.28

15.5%

2.29

16.4%

2.30

$265,000

2.31

$31.50

2.32

5%

2.33

5%

2.34

$127.50

2.35

$200.60

2.36

$100

2.37

$180

2.38

15.33%

2.39

90¢

2.40

Both cost the same $200.

2.41

You pay $42; the order does not matter.

2.42

$153

2.43

$89.76

2.44

12.2%

2.45

653

2.46

2.47

6%

2.48

$501.88

2.49

$502.85

2.50

$21,333.33

2.51

$7.67

2.52

1000 + 1000(10%)(1/12) = 1008.33

1008.33 + 1008.33(10%)(1/12) = 1016.73

1016.73 + 1016.73(10%)(1/12) = 1025.20

1025.20 – 1000 = 25.20

Answer: The interest was $25.20.

2.53

500(1 + 2% ÷ 12)¹² = 510.09

Answer: $510.09 – $500 = $10.09

2.54

700(1 + 1.5% ÷ 365)³⁶⁵ = 710.58

Answer: $710.58

2.55

12,000(1 + 12%)⁴ = 18,882.23

18,882.23 – 12,000 = 6,882.23

Answer: Barbara owes $6,882.23

2.56

6800(1 + x%)⁵ = 10,000

(1 + x%)⁵ = 1.4706

Replace x by 6, 7, 8, 9 until you get a true statement.

(1 + 8%)⁵ = 1.4693, which is approximately 1.47.

2.57

Day-to-Day: 1500(1 + 0.5%)³ = 1522.61

Interest = 1522.61 – 1500 = 22.61

Credit Union: 1500(1 + 2.72% ÷ 4)¹² = 1627.08

Interest = 1627.08 – 1500 = 127.08

127.08– 22.61 = 104.47

Answer: The Credit Union pays $104.47 more.

2.58

Bought: 100 × $10 = $1000

Sold: 100 × $12.05 = $1205

Dividend: 4 × $1.25 = $5.00

Earnings: $1205 + $5.00 – $1000 = $210

Jim’s profit was $210.

2.59

2.60

Cost + mark-up $70

Selling price: 0.85 of $70 = $59.50

Profit: $9.50

2.61

Cost: 60/1.2 = 50

Selling price 0.8 of 50 = 40

The selling price is $40.

3.1

If Elsa is x, then Thor is x + 7

Equation: x + x + 7 = 35

Elsa is 14 years old and Thor is 21 years old.

3.2

I am x and my father is x + 41.

x + 41 – 8 = 3(x + 5)

x = 9 I am 9 years old.

3.3

3.4

E + C + F = 61

E = C + 5

F = 6C

C + 5 + C + 6C = 61

8C = 56

C = 7 Carl is 7 years old.

3.5

In x years: 6 + x + 3 + x + 1 + x = 0.8(40 + x)

3x + 10 = 32 + 0.8x

2.2x = 22

x = 10 In 10 years.

3.6

Eva is 44 years old.

3.7

Susan is 12 years old and Jack is 15 years old.

3.8

If Carla is x, then Glenn is x + 6 years old.

2 (x + 6) + x = 57

x = 15 x + 6 = 21

Carla is 15 years old and Glenn is 21 years old.

3.9

Mary is 18 years old and Chris is 11 years old.

3.10

5R – 3S = S

R = S – 2

Sig is 10 years old and Ray is 8 years old.

3.11

A + V = 15

V = 1/2 A → 2V = A

2V + V = 15

3V = 15

V = 15 Victor is 5 and Adam is 10 years old.

3.12

Ina, Mina, and Mo are 24, 36, and 42 years old.

3.13

If Mark is x and Mindy is y,

then x + y = 84 and 3x = 4y.

Mark is 48 years old and Mindy is 36 years old.

3.14

Jim and Jon are 3x and 7x, respectively.

3.15

David is 8 years old.

3.16

The mother is now 38 years old.

3.17

Ellen is 10 years old.

3.18

John is 9 and Ed is 17 years old.

3.19

Ginger is 8 years old.

3.20

Bev is x and Ron is x + 6.

Bev is 30 and Ron is 36 years old.

3.21

Phil is 27 years old. Reject –27 because an age cannot be negative.

3.22

Ronald is 20 and Liz is 22 years old. Reject the negative answers.

3.23

The older daughter is 23 years old.

3.24

The first perfect square is 45² = 2025.

The mathematician will be 45 years old in 2025.

In 2006 she will be 2025 – 2006 = 19 years younger or 45 – 19 = 26.

The mathematician will be 26 years old in 2006.

3.25

S = L + 5

L² + 2S = 58

L² + 2L – 48 = 0

(L + 8)(L – 6) = 0

L =–8 Reject

L = 6 Lucy is 6 years old.

4.1

40 $3.85 stamps and 10 80¢ stamps

4.2

20 nickels and 40 dimes

4.3

32 nickels and 14 dimes

4.4

25 quarters and 2 dimes

4.5

16 liters of the 20% solution

4.6

Multiply by 100:

Add 20oz. pure acid.

4.7

The punch has 19 % (rounded) of pomegranate juice.

4.8

5 liters of water

4.9

3 liters of water

4.10

67 quarts (rounded)

4.11

Add 3.5 liters of water.

4.12

60 g of nickel

4.13

Add 200 g pure gold.

4.14

A chicken has 2 legs and a sheep has 4 legs.

Total number of heads: x + y = 22

Total number of legs; 2x + 4y = 58

Solve the system of equations:

x = 15 and y = 7

There are 15 chickens and 7 sheep.

4.15

Selma has 60 $10 bills.

4.16

There were 7 $20 bills.

4.17

An adult ticket was $320.

4.18

The gum cost 10¢ and the chocolate cost 15¢.

4.19

40 regular hours + 7 hours overtime = $390

42 regular hours + 8 hours overtime = $416

Kelly’s overtime rate is $10 per hour.

4.20

5.1

5 min.: 60 min. = 1:12

5.2

The pieces are 9 and 12 in.

5.3

3 women + 7 men = 10 total

7/10 of 4680 men = 3276

3/10 of 4680 women = 1404

There were 3276 men and 1404 women.

5.4

16 students + 1 professor = 17 total

1/17 of 3400 = 200

200 professors at the game.

5.5

8 women, 20 people, 12 men

Men: women = 12:8 = 3:2

The ratio of men to women is 3:2.

5.6

462 miles

5.7

x = 32

The cost is 32¢.

5.8

9 in.

5.9

20

5.10

100 times

5.11

x = 36

The tree is 36 ft. tall.

5.12

42 in.

5.13

3/4 lb.

5.14

18 cups.

5.15

1/2 pint

5.16

4.5 ft.

5.17

13 5/6 years

5.18

80 servings

5.19

80 square yards

5.20

1760 yards

5.21

5 lbs. peaches

2 2/9 cups apricot jam

5.22

1296 in.²

5.23

5.24

25 Tbsp. = 25/16 cups = 1 9/16 cups

5.25

7 cans

5.26

14 Tbsp. are left.

5.27

3 1/8 pints

5.28

4500 g

5.29

380 cm

5.30

80 m

5.31

3.890 kg

5.32

1.5 dm

5.33

1.50 cm²

5.34

5 mm²

5.35

75 cm²

5.36

3000 dm³

5.37

5000 cm³

5.38

50 cL

5.39

3 dm

5.40

20 small units

5.41

0.15m × 0.12 m = 15 cm × 12 cm

5.42

100 × 125 mm = 12500 mm = 12.5 m

5.43

3 × 200 mm = 600 mm = 60 cm

5.44

1 cup = 1/4 quarts = 0.946 L/4 = 9.46 dL/4 = 2.4 dL (rounded)

5.45

3.4kg = 7.48 lb.

51 cm = 20 in.

5.46

3.57oz.

5.47

29.9in.

5.48

11.6¢

5.49

5mm/sec.

5.50

40 km/hr.

5.51

$1.17

5.52

1640 ft.

5.53

5.54

5.55

The babysitter thought that the temperature was measured in Celsius degrees, not in Fahrenheit. 100°C = 212°F, the temperature of boiling water!

6.1

4 mph

6.2

They meet after 2 hours, 30 miles from Carl’s house.

6.3

The speeds are 50 and 60 mph.

6.4

The difference between the rates is 1.54 mph.

6.5

Total trip: 400 miles

200/45 hr. = 4.4 hr.

200/55 hr. = 3.6 hr.

Total time: 8 hours

Average speed: 400/8 mph = 50 mph

6.6

The car went on the dirt road for 1 hour.

6.7

They met after 1 2/7 hour or 1 hour 17 min.

The time is then 11:57.

6.8

The new time is 3/4 of the old time, or 25% shorter.

6.9

6.10

6.11

2 hours

6.12

40 minutes

6.13

x = 6

It takes Jonas 6 hours to do the job alone.

6.14

Alternate solution:

It would take Carl 24 hours to do the job alone.

6.15

120 minutes

6.16

3 R 17 cars 10 min. 1 R 17/(30) cars/min.

14 R 14(17)/30 cars/min.

14 R 14(17)45/30 cars/min.

14 robots can assemble 357 cars.

6.17

20 minutes

6.18

3 hours

6.19

It takes 20 minutes.

7.1

7.2

7.3

23 (rounded)

7.4

24 (rounded)

7.5

34.5

7.6

The shape of the bar graph and frequency polygon will depend on the frequency of heads you obtain.

7.7

7.8

7.9

7.10

7.11

7.12

Men + Women over 65: 1,543,332

Total population: 8,837,496

7.13

7.14

7.15

6/10 = 3/5, or 0.6

7.16

Total number of minutes in 24 hours: 1440 minutes.

Equal digits: 1.11,2.22, 3.33,4.44, 5.55, 11.11.

11.11 occurs once, the others twice during 24 hours.

Probability: 11/1440 = 0.0076 or 0.76%

7.17

1/52

7.18

6/52 = 3/26, or 11.53%

7.19

7.20

7.21

7.22

3:3 = 1:1

7.23

3:3 = 1:1

7.24

7.25

30% × 30% = 9%

7.26

7.27

7.28

7.29

7.30

7.31

7.32

7.33

7.34

7.35

534 × 216 = 115,344 dates

7.36

(3)(3)(3) = 27

7.37

5 × 4 × 3 × 2 × 1 = 120 ways

7.38

(2)(3)(2)(1) = 12

7.39

(3)(2)(1)(1) = 6

7.40

CIRCLE has 6 letters but 2 are the same. The number of arrangements is 6!/2! = 360

7.41

{2,4,6, ...}

7.42

7.43

36 students are taking German.

7.44

14 people could both sing and dance.

7.45

20 cars have both an airbag and a car phone.

8.1

8.2

8.3

8.4

8.5

20 in.

8.6

8.7

14.4 in.

8.8

13 cm, 26 cm, and 21 cm

8.9

36 in.

8.10

20.25 in.²

8.11

The area is 4 in.²

8.12

The sides are 4 in. and 8 in.

8.13

Area of rectangle: 11.2 × 6 = 67.2

The area is 5% larger.

8.14

8 in.

8.15

b = 12 inches

8.16

10 units

8.17

25 units

8.18

The area is 6 in.²

3b/2 = 6

b = 4

This is a right triangle with the legs 3 in. and 4 in.

8.19

The missing leg is 4 units

8.20

The ladder is 18.3 ft. up on the wall.

8.21

8.22

A = 90°

8.23

The angles are 48° and 80°.

8.24

A + B = 156

A = C

A + B + C = 180

Angle B = 132°

8.25

x = 10

8.26

x = 4.5

8.27

The sides are 15 and 18 cm.

8.28

The tree is 36 ft.

8.29

12/9 = 4/3

The area is 1 1/3 in.²

8.30

r = 10

8.31

π · 1.5 · = 2 = 3π cm or about 9.4 cm.

8.32

The area is approximately 3.5 in.² and the perimeter is 7.7 inches.

8.33

R = 5/8 in.

r = 3/8 in.

The area of the ring is R² – r².

The area is π/4 sq. in. or 0.79 in.².

8.34

142 in.²

8.35

600 in.²

8.36

204.48 in.²

8.37

60p + 2(9p) = 78p

The total surface area is 78π in.², or

245 in.².

8.38

125 cm³

8.39

25πh = 290

h = 3.7 cm (approximately)

8.40

π(4)(7) = 28π or 88

88 in.³

8.41

8.42

8.43

sin 30° = x/20

x = 10

8.44

tan α = 5/5

α = 45

The angle is 45°

8.45

tan 60 = x/20

x = 34.6

The length of the flagpole is 34.6 ft.

8.46

A is on the + y-axis

B is on the – x-axis

C is the origin where the axes cross

D is in the IV quadrant

E is in the II quadrant

F is in the III quadrant

8.47

When the x-numbers are equal, the line between points is vertical.

When the y-numbers are equal, the line is horizontal.

8.48

8.49

8.50

8.51

8.52

10 × 3/2 = 15

15 square units

8.53

(13 – 5)(6 – 2) = 8(4) = 32

32 square units

8.54

Use the example as a model.

The rectangle is 70.

The triangles are 2, 6, 12, 13.5.

The polygon is 36.5 square units.