Math
Summer
Pack
Name: Date: Lesson 1.2 Writing Rational Numbers as Decimals
Using long division, write each rational number as a terminating
decimal.
1.
654
7
2. 15
16
3. 9
126
4. 24
35
Using long division, write each rational number as a repeating decimal
with 2 decimal places. Identify the pattern of repeating digits using bar
notation.
© Marshall Cavendish International (Singapore) Private Limited.
5.
28
1
6. 8
9
15
7. 56
5
2
8. 6
11
Extra Practice Course 2A 3
(M)MIFEP_C2A_Ch01.indd 3
20/06/12 12:08 PM
Name: Date: Write each rational number as a repeating decimal using bar notation.
You may use a calculator.
9.
5
11
11. 456
123
10. 12.
9
13
166
91
Refer to the list of rational numbers below for questions 13 to 16. You
may use a calculator.
2
11 90 63
171
13
,
,
, , 4
17 19 10
112
18
13. Write each rational number as a decimal with at most 4 decimal places.
15. Place each rational number on the same number line.
16. Which rational number is farthest from 0?
© Marshall Cavendish International (Singapore) Private Limited.
14. Using your answers in question 13, list the numbers from least to greatest using
the symbol .
4 Chapter 1 Lesson 1.2
(M)MIFEP_C2A_Ch01.indd 4
20/06/12 12:08 PM
Answers
19.
2.5°C
6
4
Chapter 1
Lesson 1.1
1.
0
2
2
3°C
20.
3
4
40
0
1
21.
0.8°C
40
41
3
unit
4
39
2
5
38
47
2. 12
65
22.
1
2
3.5°C
7°C
38
37
66
21
3
4
23.
67
22
23
24.
13
0
1
47
12
11
12
8
7
6
unit
13
0
1
32
26.
33
50
49
49.9
12
units
5
4
© Marshall Cavendish International (Singapore) Private Limited.
25.
79
11
32.4
6
13
12
4. − 5
261
7
135
6
6
3. −
2
27. 4
0
4
12
5
12
67
67 67
, or
6.2 ,
1
1
1
1
5
375
7. 8.
12
7
59
22
22 22
, or
9. 10.2 ,
18
21 21
21
869
869 869
37
,
, or
11. 12.2
3
12
12
12
1
251
13. 2 14.
100
699
27
27 27
,
, or
15.
16. 2
200
200 200
200
138
138 138
33
33 33
17. 2 ,
18.
2
,
, or
, or
25
25
25
25 25
25
5.
8
1
66
3
47
units
12
6
5
6
3
4
0
4
ºC
5
22
21
, , 3.12, 1.01, , 6.7
14
7
4
5
14 3.12
5 4 3
2 1
22
7
0
1
2
3
4
1.01
5
21
4
6
7
6.7
Lesson 1.2
1.
654
7
43.6
0.4375 2.
15
16
0.4375
16 7.0000
6 4 60
48 120
112 80
80
0
)
43.6
15 654.0
60 54
45 90
90
0
)
Extra Practice Course 2A 87
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 87
02/07/12 9:04 PM
Lesson 1.3
126
)
1.
)
2.
3.
4.
1
121
5. 28 3.1 6. 8 15 15
9
)
)
3
4
√10
21 is between 4 and 5.
4
5
√21
37 is between 6 and 7.
7
4
2
√14
3
6
√27
5
9
√68
9. 51 5 7.141…
7.141 is closer to 7.1 than to 7.2.
So, 51 is closer to 7.1.
8
8. 2 68 is between 28 and 29.
0.1818
11 2.0000
1 1 90
88 20
11 90
88
2
56.83
56.833
6 341.000
30
41
36 50
48
20
18
20
18
2
10 is between 3 and 4.
7. 2 27 is between 25 and 26.
11
6
3
√8
3
√8
14
6. 2
is between 23 and 24.
)
7. 56 5 341 8. 2 0.18
6
2
6 √37
5. 2 8 is between 22 and 23.
8.06
8.066
15 121.000
120 1 00
9 0
1 00
90
10
3.11
9 28.00
27 10
9 10
9
1
8 is between 2 and 3.
7.1
√51
7.2
10. 2 279 5 216.703…
216.703 is closer to 216.7 than to 216.8.
So, 2 279 is closer to 216.7.
√279
16.8
16.7
11. 3 888 5 9.612…
9.612 is closer to 9.6 than to 9.7.
3
888 is closer to 9.6.
So, 9.6 √888
12. 99 5 9.94987…
9.95 is closer to 9.9 than to 10.0.
99 is closer to 9.9.
So, 9.7
3
9.0.45
10. 20.692307
11. 23.70731
12.1.824175
13. 22.6471, 4.7368, 6.3000, 21.5268, 4.7222
11
171
90
63
14. 2

 4 13 

112
17
19
10
18
15.
2
11
171
17
112
4
13
18
9.9
10.0
√99
13. 2 1999 5 244.71017…
244.71 is closer to 244.7 than to 244.8.
So,2 1999 is closer to 244.7.
63
10
√1999
3
2
1
0
1
2
3
4
5
90
19
16.
63
10
88 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 88
6
7
44.8
© Marshall Cavendish International (Singapore) Private Limited.
9
3.6
3. 24 0.375 4. 35
0.375
3.6
24 9.000
35 126.0
72
105 180
210
168 210
120
0
120
0
44.7
14. 6655 5 81.57818…
81.58 is closer to 81.6 than to 81.5.
So, 6655 is closer to 81.6.
81.5
√6655
81.6
02/07/12 9:04 PM
Name: Date: Lesson 2.4 Operations with Integers
Evaluate each expression.
1. 25  8 1 12 2.20 2 4  (26)
3. 3  (29) 1 (22)  (7) 4.150  (25) 1 (238)
5. 248  4  (25) 2 17 6. 235 2 490  7 1 12
9. 90  (26 2 3) 1 45
10.(16 1 2)(3) 2 5(25 1 3)
11. 230 1 5(3 1 8) 2 45
12.25  [24 1 (21)] 2 9(3)
13. 36  6 2 (225 1 15)(4)
14. 242 1 70  (22 2 3) 1 84  (4 1 2)
15. 2200 1 32(23 1 7) 2 45(15 2 20)
16.480  (6 1 14) 2 7(4) 1 8(3 1 4)
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7. 82 2 (9 2 13)  9 8. 227 2 (4 1 4)  3
18 Chapter 2 Lesson 2.4
(M)MIFEP_C2A_Ch02.indd 18
20/06/12 12:09 PM
Name: Date: Solve. Show your work.
17. Cecilia has an 8-inch by 12-inch sheet of rectangular
paper. She cuts out identical 4-inch by 3-inch
rectangles from two corners of the paper. She then
cuts out identical right triangles from the other
two corners of the paper. Using the diagram shown,
find the area of the remaining paper.
4 in.
4 in.
8 in.
2 in.
12 in.
© Marshall Cavendish International (Singapore) Private Limited.
18. Today, a tank contains 6,600 gallons of water. For the past 3 days,
210 gallons of water was pumped out of the tank each day. What was the
volume of water in the tank 3 days ago?
Extra Practice Course 2A 19
(M)MIFEP_C2A_Ch02.indd 19
20/06/12 12:09 PM
32. Total change in the stock’s value
5 22  7 5 2$14
The total change in the stock’s value is 2$14.
Lesson 2.3
Lesson 2.4
1.7  (29) 5 263
2.12  (28) 5 296
3. 23  115 233
4. 25  6 5 230
5. 26  (28) 5 48
6. 27  (215) 5 105
7. 230  (0) 5 0
8.0  (219) 5 0
9.4  (26)  (10) 5
224  10
5 2240
10.7  8  (29) 5
56  (29)
5 2504
11. 211(5)(24) 5
255  (24)
5 220
12. 22(221)(3) 5
42  3
5 126
13.6(214)(217) 5
284  (217)
5 1,428
14. 24(228)(29) 5
112  (29)
5 21,008
15. 23(212)(210) 5
36  (210)
5 2360
16. 28(0)(227) 5 0
17. 250(26)(0) 5 0
18. 29(28)(2)(3) 5
72  2  3
5 144  3
5 432
19. 25(7)(24)(25) 5
235  (24)  (25)
5 140  (25)
5 2700
20. 210(23)(26)(22) 5
30  (26)  (22)
5 2180  (22)
5 360
21.357  (27) 5 251 22.560  (216) 5 235
23. 2720  12 5 260 24. 2550  11 5 250
25. 2189  (29) 5 21 26. 2112  (24) 5 28
27.0  (220) 5 0
28.0  (25) 5 0
29. Change in altitude per minute
5 22,250  15
5 2150 ft/min
The change in altitude per minute is
2150 ft per/min.
30. Distance 5
22  40
5 280 ft
He is 80 feet below sea level after 40 minutes.
31. Average change in sales income per
month 5
$9,000,000  3
5 $3,000,000
The average change in sales income is
$3,000,000 per month.
1. 25  8 1 12
2.20 2 4  26
5 240 1 12
5 20 2 (224)
5 228 5 20 1 24
5 44
3.3  (29) 1 (22)  7 4.150  (25) 1 (238)
5 227 1 (214)5 230 1 (238)
5 241 5 268
5. 248  4  (25) 2 17
5 248  (220) 2 17
5 2.4 2 17
5 214.6
6. 235 2 490  7 1 12
5 235 2 70 1 12
5 2105 1 12
5 293
7.82 2 (9 2 13)  9
5 82 2 (24)  9
5 82 2 (236)
5 82 1 36
5 118
8. 227 2 (4 1 4)  3
5 227 2 8  3
5 227 2 24
5 251
9.90  (26 2 3) 1 45
5 90  (29) 1 45
5 210 1 45
5 35
10.(16 1 2)(3) 2 5(25 1 3)
5 (18)(3) 2 5(22)
5 54 2 (210)
5 54 1 10
5 64
11. 230 1 5(3 1 8) 2 45
5 230 1 5(11) 2 45
5 230 1 55 2 45
5 275 1 55
5 220
12.25  [24 1 (21)] 2 9(3)
5 25  (25) 2 9(3)
5 25  (25) 2 27
5 25 2 27
5 232
13.36  6 2 (225 1 15)(4)
5 36  6 2 (210)(4)
5 36  6 2 (240)
5 6 2 (240)
5 6 1 40
5 46
© Marshall Cavendish International (Singapore) Private Limited.
25.480 2 570 5
480 1 (2570)
5 290
Simon’s final score was 290 points.
92 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 92
02/07/12 9:04 PM
14. 242 1 70  (22 2 3) 1 84  (4 1 2)
5 242 1 70  (25) 1 84  6
5 242 2 14 1 14
5 242 1 0
5 242
15. 2200 1 32 (23 1 7) 2 45(15 2 20)
5 2200 1 32(4) 2 45  (25)
5 2200 1 128 2 (2225)
5 2200 1 128 1 225
5 272 1 225
5 153
16.480  (6 1 14) 2 7  (4) 1 8  (3 1 4)
5 480  20 2 7  4 1 8  7
5 480  20 2 28 1 56
5 24 2 28 1 56
5 24 1 56
5 52
17. Area of remaining paper:
Area of original paper 2 Area of two cut-out
triangles 2 Area of two cut-out rectangles
5 12  8 2 2 
1
442243
2
5 96 2 16 2 24
5 56 in2
The area of the remaining paper is
56 square inches.
18. Volume of water pumped out over 3 days
5 3  210
5 630 gal
Water volume 3 days ago 5 6,600 1 630
5 7,230 gal
The volume of water in the tank 3 days ago
was 7,230 gallons.
Lesson 2.5
8
3
© Marshall Cavendish International (Singapore) Private Limited.
1. 2.
1
8 4
1 3
4
3 4
43
32
3
12
12
32 3
12
29
12
5
2
12
 7
4
4
7
  15  9 
15
9
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 93
43
7 5
15 3
95
12
35
45
45
12 35
45
23
45
3. 4.
7
4
43
7
15
5
15
53
7 12
15
15
7 12
15
5
15
1
3
5  1 
5
1
   3
8
8
3
1 8
5 3
83
38
15
8
24
24
15 8
24
23
24
2
2
5
 5
5. 3  9  3 9
23
5
33
9
6
5
9
9
65
9
11
9
2
1
9
1  2 
1
2
6. 6  3  6 3
1
22
6
32
1
4
6
6
1 4
6
5
6
1
2
1 3
2
7. 5 15 5 3 15
3
2
15
15
3 2
15
5
15
1
3
Extra Practice Course 2A 93
02/07/12 9:04 PM
Name: Date: Lesson 2.5 Operations with Rational Numbers
Evaluate each expression. Give your answer in simplest form.
8
3
1. 

1
2. 4  7 
4
 9
15
 1
5
3. 7 4 4.  
 3
8
15
5
5.
 5
 2
2
1
  6.  
 9
 3 
3
6
1
3
7. 1 2 8.
7
15
14
9.
 1
3
   2
4
 3  5
2
10.    4  8
5
11.
 2 3
1
   5 4
3
12.
 1  3 
2
   
3  5 
9
14.
 5   1
4
   
 6  3
9
 3  5
5
13. 2    4  8
6
© Marshall Cavendish International (Singapore) Private Limited.
5
20 Chapter 2 Lesson 2.5
(M)MIFEP_C2A_Ch02.indd 20
20/06/12 12:09 PM
Name: Date: Evaluate each product. Give your answer in simplest form.
15. 3 5 4
17. 12
14  3 
1  25  7 
19. 2 2 3 3  3 
4
16. 2 1 8
4
18. 1
20.
27
8 
2
2 
27 
5
2  2
1 
15  3 
Evaluate each quotient. Give your answer in simplest form.
1
4
© Marshall Cavendish International (Singapore) Private Limited.
21. 3
8
22.
 4
2
 
 35 
5
 5
1
23.    18 
6

2
1
24. 1 3 
 3
3


25. 2 3 1 3   8
4
26.
27.
29.
2
 
3
16
28.
 4
 
 5
 7
 
 20 
30.
10
5
 
 13 
7
 
8
 3
 
 4
 2
2 
 5
 1
1 
 5
Extra Practice Course 2A 21
(M)MIFEP_C2A_Ch02.indd 21
20/06/12 12:09 PM
Name: Date: Solve. Show your work.
31. A restaurant used 8 5 pounds of rice on Monday and 5 1 pounds of rice
6
6
on Tuesday. How many more pounds of rice was used on Monday than on
Tuesday?
32. Janet has 9
1
2
feet of cloth. She needs to cut it into lengths of
feet.
3
3
How many complete lengths can she cut?
33. A recipe calls for 2 1 cups of walnuts. Only 5 cup of walnuts are on hand.
6
2
How many more cups of walnuts does a chef need for the recipe?
34. The sum of two rational numbers is 8 1 . If one of the numbers is 5 2 ,
4
3
35. Parcel P weighs 4 1 pounds, Parcel Q weighs 3 2 pounds and Parcel R
weighs 6
5
2
4
pounds. Find the average weight of the three parcels.
5
© Marshall Cavendish International (Singapore) Private Limited.
find the other number.
22 Chapter 2 Lesson 2.5
(M)MIFEP_C2A_Ch02.indd 22
20/06/12 12:09 PM
14. 242 1 70  (22 2 3) 1 84  (4 1 2)
5 242 1 70  (25) 1 84  6
5 242 2 14 1 14
5 242 1 0
5 242
15. 2200 1 32 (23 1 7) 2 45(15 2 20)
5 2200 1 32(4) 2 45  (25)
5 2200 1 128 2 (2225)
5 2200 1 128 1 225
5 272 1 225
5 153
16.480  (6 1 14) 2 7  (4) 1 8  (3 1 4)
5 480  20 2 7  4 1 8  7
5 480  20 2 28 1 56
5 24 2 28 1 56
5 24 1 56
5 52
17. Area of remaining paper:
Area of original paper 2 Area of two cut-out
triangles 2 Area of two cut-out rectangles
5 12  8 2 2 
1
442243
2
5 96 2 16 2 24
5 56 in2
The area of the remaining paper is
56 square inches.
18. Volume of water pumped out over 3 days
5 3  210
5 630 gal
Water volume 3 days ago 5 6,600 1 630
5 7,230 gal
The volume of water in the tank 3 days ago
was 7,230 gallons.
Lesson 2.5
8
3
© Marshall Cavendish International (Singapore) Private Limited.
1. 2.
1
8 4
1 3
4
3 4
43
32
3
12
12
32 3
12
29
12
5
2
12
 7
4
4
7
  15  9 
15
9
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 93
43
7 5
15 3
95
12
35
45
45
12 35
45
23
45
3. 4.
7
4
43
7
15
5
15
53
7 12
15
15
7 12
15
5
15
1
3
5  1 
5
1
   3
8
8
3
1 8
5 3
83
38
15
8
24
24
15 8
24
23
24
2
2
5
 5
5. 3  9  3 9
23
5
33
9
6
5
9
9
65
9
11
9
2
1
9
1  2 
1
2
6. 6  3  6 3
1
22
6
32
1
4
6
6
1 4
6
5
6
1
2
1 3
2
7. 5 15 5 3 15
3
2
15
15
3 2
15
5
15
1
3
Extra Practice Course 2A 93
02/07/12 9:04 PM
5  3 
5
5
3
5
  6
4
8
6
4
8
5 4
36
53
64
46
83
20
18
15
24
24
24
20 18 15
24
23
24
9.
−1 2
1
3
3
7
14
7 2
14
−2
3
14
14
2 3
14
5
14
14.
4  5   1
4
5
1
    6  3
9
9
6
3
42
53
1 6
92
63
36
8
15
6
18
18
18
8 15 6
18
29
18
11
1
18
1 2
3
−3
 1
  4
2
4
22
−3
2
4
4
3 2
4
1
4
 
10. 2  3  5 2 3 5
5  4  8
5
4
8
28
3 10
55
58
4 10
85
16
30
25
40
40
40
16 30 25
40
11
1
40
3
4
15. 5
16
1 8
9 8
16. 2 4 27 4 27
1
1  2 3
1 2
3
11.   3  5 4
3
5
4
1 20
2 12
3 15
3 20
5 12
4 15
20
24
45
60
60
60
20 + 24 − 45
60
1
60
1
3
2
−2
 1  3 
12. 9  3   5  9 3 5
1 15
2 5
39
95
3 15
59
10
15
27
45
45
45
10 15 27
45
32
45
1 3 5
5
12
4 12 4
5  3 
5
5
3
5
  6
4
8
6
4
8
5 4
36
53
64
46
83
20
18
15
24
24
24
20 18 15
24
23
24
94 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 94
1 4 17. 2
27 3
2
3
14 
3
14
10
1   
25 
7
25  7 
2
2
14 10
25 7 1
5
4
5
8 
2
35  12 
18. 1  2  27
5
27  5 
7
13.
9 8
35 12
4
27 5 1
9
28
9
1
3
9
2
3
8
15
19. 2  3   




3
4
3
2
8 15
1
4
5
© Marshall Cavendish International (Singapore) Private Limited.
8.
3 41
10
02/07/12 9:04 PM
27.  2 
3
2
16)
16 3 (
2 
2
2  5
1  20.
15 
3
15  3 
2 5
3
1
4
2
9
1 8
1
28.
2
4 3
2
3
 7
 
8
 3
 
 4
2  4
2  35 
  5  35 
5
4
1
2 35
7
7  4
 
8  3
3
6 5
3
5
2 
1
5  10 
24. 1 3 3 
3
3  3
© Marshall Cavendish International (Singapore) Private Limited.
5 3
3
 3
 11  11
25. 2  1     
4
8
4
8
1
1
2
26. 10 10 5
13
5
13 
13
10 5
11  8 
. 4  11
11 8
1 5 1
15
4
7
44
1 7
30. 
2
 2 5 
12
6
5
5
 1
15 
2
4 111
12 5
5
6
2
12 5
1
1
5 61
2
31. Amount of rice used on Monday 2
Amount of rice used on Tuesday:
5
6
8 5
2
10 13
26
4 20
16
7
2
2
7
1
2
8 3
1
1 3 10 2
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 95
5  3
 
10
3
1
1
29.  4 
 
 5
4  7
 
5  20 
 7
 
20


4  20 
 
5  7
74
7
6
1
1
6
1  5
1  18 
23.    
6  18 
6  5
1
1
2
1 18
7  3
 
8  4
2
7
2
3
1
24
5 42
1
2
1
3 16 8
3
1 8
8
4 3
22.
1
15 3
21. 1
1
53
31
6
6
6
53 31
6
22
6 Extra Practice Course 2A 95
2
3 lb
3
02/07/12 9:04 PM
1
2
2
5
4 3 6
1
53
31
6
6
6
53 31
6
22
6
2
3 lb
3
2
3 pounds more rice was used on Monday
3
than on Tuesday.
32. Number of complete lengths she can cut:
2
3
9 147
3
10
147 1
10 3
Average weight 1
29 3
3
3 1
49
29
She can cut 29 complete lengths.
33. Number of cups:
1
2
5
5
5
6
2
6
53
5
23
6
15
5
6
6
15 5
6
10
6
2
1 c
3
2
The chef needs 1 more cups of walnuts.
3
34. The other number: 1 
2
33
17
8  5  4
3
4
3
33 3
17 4
43
3 4
99
68
12
12
99 68
12
31
12
7
2
12
The other number is 2
1
2
2
5
7
.
12
35. Total weight 4 3 6
96 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 96
4
5
9
17
34
2
5
5
95
17 2
34 2
25
52
52
45
34
68
10
10
10
45 34 68
10
147
lb
10
147 1
10 3 1
49
10
9
4 lb
10
2 9
17
34
2
5
5
95
17 2
34 2
25
52
52
45
34
68
10
10
10
45 34 68
10
147
lb
10
The average weight of the three parcels is
4
9
pounds.
10
Lesson 2.6
1.|7.9| 2 |23.15| 5
7.9 2 3.15
5 4.75
The sum is positive, because 7.9 has a
greater absolute value.
23.15 1 7.9 5 4.75
2.|25.3| 2 |0.072| 5
5.3 2 0.072
5 5.228
Use a negative sign, because 25.3 has a
greater absolute value.
0.072 1 (25.3) 5 25.228
3.|241.36| 1 |28.2| 5
41.36 1 8.2
5 49.56
Use the common sign, a negative sign, for
the sum.
241.36 1 (28.2) 5 249.56
4.8.22 2 (20.355) 5
8.22 1 0.355
5 8.575
5.|217.203| 1 |20.86| 5
17.203 1 0.86
5 18.063
Use the common sign, a negative sign, for
the sum.
217.203 2 0.86 5 218.063
6. 229.5 2 (29.34) 5 229.5 1 9.34
|229.5| 2 |9.34| 5
29.5 2 9.34
5 20.16
Use a negative sign, because 29.5 has a
greater absolute value.
229.5 2 (29.34) 5 220.16
7.0.4  (25.7) 5 22.28
8. 22.7  3.1 5 28.37
9. 24.36  (21.8) 5 7.848
10.3.04  (26.3) 5 219.152
11. 236.9  4.5 5 28.2
© Marshall Cavendish International (Singapore) Private Limited.
5
6
8 5
4
5
02/07/12 9:04 PM
Name: Date: Lesson 2.6 Operations with Decimals
Evaluate each sum or difference.
1. 23.15 1 7.9 2.0.072 1 (25.3)
3. 241.36 1 (28.2) 4.8.22 2 (20.355)
5. 217.203 2 0.86 6. 229.5 2 (29.34)
Evaluate each product.
7. 0.4  (25.7) 8. 22.7  3.1
9. 24.36  (21.8)
10.3.04  (26.3)
© Marshall Cavendish International (Singapore) Private Limited.
Evaluate each quotient.
11. 236.9  4.5
12.159.12  (23.4)
13. 249.14  (26.3)
14.12.376  0.52
Evaluate each expression.
15. 20.48 1 (20.1) 1 (22.3)
16. 23.59 1 16.7 1 (2150.06)
17. 49.03 1 (27.8) 2 (221.05)
18.601.03 2 467.9 1 (28.12)
19. 21.4 2 6.2 1 4.2  0.3 2 2.6
20.(39.3 1 6)  3 1 0.8  4
Extra Practice Course 2A 23
(M)MIFEP_C2A_Ch02.indd 23
20/06/12 12:09 PM
Name: Date: Solve. Show your work.
21. On Sunday, the balance in Christina’s savings account was $315.12. On
Monday, she makes withdrawals of $78.95 and $143.80. On Tuesday, she
deposits $63.79. What is her balance after she makes the deposit?
22. The table shows the activity in George’s savings account.
Date
Deposit
Withdrawal
Balance
January 31
2
2
$148.20
February 5
$35.65
$182.30
$1.55
February 18
$120.83
$78.32
?
What is the balance in George’s account on February 18?
24. In 2010, a company reported a net income loss of $23,800,000. In 2011, the
company reported a net income gain of $10,400,000. How much more did
the company earn in 2011 than in 2010?
25. Fiona has only $10 to pay the fees for three art projects. The fees of the
projects are $2.50, $6.75, and $2.80. How much more money does
she need?
26. In Fairbanks, Alaska, the average temperature in January is 29.7°F. The
average temperature in July is 62.4°F. On average, how many degrees
colder is Fairbanks in January than in July?
© Marshall Cavendish International (Singapore) Private Limited.
23. The highest temperature recorded was 118.4ºF in Athens in 1977. The
lowest temperature recorded in Ust Shchugor was 191ºF lower than that
of the highest temperature recorded. What is the lowest temperature
recorded?
24 Chapter 2 Lesson 2.6
(M)MIFEP_C2A_Ch02.indd 24
20/06/12 12:09 PM
Name: Date: 27. A buyer purchased 6 baseball hats for $76.50. The hats will be sold in his
retail store for a profit. If he plans to price each hat to make a 40% profit,
what should be the selling price of each hat?
28. What is the discount price of a skateboard that costs $155.80 if it is on sale
for 20% off?
29. The table shows the temperatures for the first 5 days of January in Lansing,
Michigan. Find the average temperature for these 5 days.
January
© Marshall Cavendish International (Singapore) Private Limited.
Temperature (°C)
1
2
3
4
5
25.2
26.7
29.1
210.3
28.6
30. Wendy has $50. She wants to buy a book that costs $26.50 and a bag that
costs $19.50. The sales tax in her state is 6%. Does Wendy have enough
money to buy the book and the bag? If so, how much money does she
have left? If not, how much more money does she need?
Extra Practice Course 2A 25
(M)MIFEP_C2A_Ch02.indd 25
20/06/12 12:09 PM
1
2
2
5
4 3 6
1
53
31
6
6
6
53 31
6
22
6
2
3 lb
3
2
3 pounds more rice was used on Monday
3
than on Tuesday.
32. Number of complete lengths she can cut:
2
3
9 147
3
10
147 1
10 3
Average weight 1
29 3
3
3 1
49
29
She can cut 29 complete lengths.
33. Number of cups:
1
2
5
5
5
6
2
6
53
5
23
6
15
5
6
6
15 5
6
10
6
2
1 c
3
2
The chef needs 1 more cups of walnuts.
3
34. The other number: 1 
2
33
17
8  5  4
3
4
3
33 3
17 4
43
3 4
99
68
12
12
99 68
12
31
12
7
2
12
The other number is 2
1
2
2
5
7
.
12
35. Total weight 4 3 6
96 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 96
4
5
9
17
34
2
5
5
95
17 2
34 2
25
52
52
45
34
68
10
10
10
45 34 68
10
147
lb
10
147 1
10 3 1
49
10
9
4 lb
10
2 9
17
34
2
5
5
95
17 2
34 2
25
52
52
45
34
68
10
10
10
45 34 68
10
147
lb
10
The average weight of the three parcels is
4
9
pounds.
10
Lesson 2.6
1.|7.9| 2 |23.15| 5
7.9 2 3.15
5 4.75
The sum is positive, because 7.9 has a
greater absolute value.
23.15 1 7.9 5 4.75
2.|25.3| 2 |0.072| 5
5.3 2 0.072
5 5.228
Use a negative sign, because 25.3 has a
greater absolute value.
0.072 1 (25.3) 5 25.228
3.|241.36| 1 |28.2| 5
41.36 1 8.2
5 49.56
Use the common sign, a negative sign, for
the sum.
241.36 1 (28.2) 5 249.56
4.8.22 2 (20.355) 5
8.22 1 0.355
5 8.575
5.|217.203| 1 |20.86| 5
17.203 1 0.86
5 18.063
Use the common sign, a negative sign, for
the sum.
217.203 2 0.86 5 218.063
6. 229.5 2 (29.34) 5 229.5 1 9.34
|229.5| 2 |9.34| 5
29.5 2 9.34
5 20.16
Use a negative sign, because 29.5 has a
greater absolute value.
229.5 2 (29.34) 5 220.16
7.0.4  (25.7) 5 22.28
8. 22.7  3.1 5 28.37
9. 24.36  (21.8) 5 7.848
10.3.04  (26.3) 5 219.152
11. 236.9  4.5 5 28.2
© Marshall Cavendish International (Singapore) Private Limited.
5
6
8 5
4
5
02/07/12 9:04 PM
© Marshall Cavendish International (Singapore) Private Limited.
12.159.12  (23.4) 5 246.8
13. 249.14  (26.3) 5 7.8
14.12.376  0.52 5 23.8
15. 20.48 1 (20.1) 1 (22.3)
5 20.58 1 (22.3)
5 22.88
16. 23.59 1 16.7 1 (2150.06)
5 13.11 1 (2150.06)
5 2136.95
17.49.03 1 (27.8) 2 (221.05)
5 49.03 2 7.8 1 21.05
5 49.03 1 21.05 2 7.8
5 70.08 2 7.8
5 62.28
18.601.03 2 467.9 1 (28.12)
5 133.13 2 8.12
5 125.01
19.21.4 2 6.2 1 4.2  0.3 2 2.6
5 21.4 2 6.2 1 1.26 2 2.6
5 15.2 1 1.26 2 2.6
5 16.46 2
­ 2.6
5 13.86
20.(39.3 1 6)  3 1 0.8  4
5 45.3  3 1 0.8  4
5 15.1 1 0.8  4
5 15.1 1 3.2
5 18.3
21. Her balance
5 $315.12 2 Withdrawals 1 Deposits
5 $315.12 2 $78.95 2 $143.80 1 $63.79
5 $236.17 2 $143.80 1 $63.79
5 $92.37 1 $63.79
5 $156.16
After the deposit, her balance is $156.16.
22. George’s balance:
5 $1.55 1 $120.83 2 $78.32
5 $122.38 2 $78.32
5 $44.06
Date
February
18
Deposit
Withdrawal
Balance
$120.83
$78.32
$44.06
The balance in George’s account on February
18 is $44.06.
23.118.4 2 191 5 272.6°F
The lowest temperature recorded was
272.6°F.
24.Difference
5 $10,400,000 2 (2$23,800,000)
5 $34,200,000
The company earned $34,200,000 more in
2011 than in 2010.
25. Total fees 5
$2.50 1 $6.75 1 $2.80
5 $12.05
$12.05 2 $10 5 $2.05
She needs $2.05 more.
26. Difference in temperature
5 Temperature in July 2 Temperature in
January
5 62.4 2 (29.7)
5 62.4 1 9.7
5 72.1°F
Fairbanks is 72.1°F colder in January than
in July.
27. Cost price of a hat 5
$76.50  6
5 $12.75
40% Profit 5
0.4  $12.75
5 $5.10
Selling Price 5
Cost Price 1 Profit
5 $12.75 1 $5.10
5 $17.85
The selling price of each hat should be
$17.85.
28. Original Price 5 $155.80
20% discount 5
0.2  $155.80
5 $31.16
Discount price 5 $155.80 2 $31.16
5 $124.64
The discount price is $124.64.
29. Average temperature
5
Sum of temperatures
5
5.2 (6.7) (9.1) (10.3) (8.6 )
5
39.9
5
5 27.98°C
The average temperature for these 5 days is
27.98°C.
30. Total cost of the book:
$26.50 1 6% Sales tax
5 $26.50 1 0.06  $26.50
5 $26.50 1 $1.59
5 $28.09
Total cost of the bag:
$19.50 1 6% sales tax
5 $19.50 1 0.06  $19.50
5 $19.50 1 $1.17
5 $20.67
Total cost 5 $28.09 1 $20.67
5 $48.76
Amount she has left 5 $50 2 $48.76
5 $1.24
She has $1.24 left.
Extra Practice Course 2A 97
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 97
02/07/12 9:04 PM
Name: Date: Lesson 3.4 Expanding Algebraic Expressions
1.
1
1
(8x 1 16) 2.
(3p 1 12)
4
3
3.
1
1
(14k 2 10) 4.
(8a 2 24)
2
8
5.
1
1
(4p 1 1) 6.
(2a 1 5)
2
7
7.
1
3
(3b 2 2) 8.
(2k 2 15)
5
5
9. 2(6x 1 0.1)
10.5(0.3y 1 2)
11. 0.3(5x 1 3)
12.0.4(2h 1 7)
13. 0.6(m 2 4)
14.0.5(p 2 3)
15. 0.2(1.2d 1 0.3)
16.1.5(0.4x 2 1.3)
© Marshall Cavendish International (Singapore) Private Limited.
Expand each expression.
40 Chapter 3 Lesson 3.4
MIF_ExtraPractice C2_Ch03.indd 40
08/12/11 11:47 AM
Name: Date: Expand each expression with a negative factor.
17. 23(x 1 2)
18. 25(2x 1 3)
19. 22(3a 1 7b)
20. 27(4k 2 h)

1
21. 6  p 3 
2
1
1
22. 2 8x 2 
4
3
23. 23(4k 1 1.2)
24. 24(0.3m 1 7)
25. 25(q 2 0.6)
26. 20.2(0.6y 2 2)
© Marshall Cavendish International (Singapore) Private Limited.
Expand and simplify each expression.
27. 2(3y 1 2) 1 5
28.4(3a 1 1) 2 2
29. 3(x 1 8) 1 5x
30.7(b 1 4) 2 3b


31. 3  1 a 1 2 1 5 4

1
 1
32. 6  a 2 3 2 a
 12
 2
Extra Practice Course 2A 41
MIF_ExtraPractice C2_Ch03.indd 41
08/12/11 11:47 AM
Name: Date: 33. 0.4(x 1 3) 1 0.8x 34.0.3(y 1 5) 2 0.1y
35. 23(5m 1 1) 2 m
36.12 2 4(n 2 2)
37. 20.6(r 1 4) 1 2.5r
38. 2(1.4x 1 5) 1 1.7x
39. 15y 1 4(8y 1 x)
40.9a 1 7(2a 2 b)
41. 6g 1 8(v 2 g)
42.12p 1 10(p 2 2q)
43. 7(2a 1 b) 1 2(3a 1 b)
44.4(2m 2 n) 1 8(3n 2 m)
45. 5(3d 1 e) 2 4(d 2 4e)
46.6(4q 2 p) 2 (2q 2 5p)
47. 23(x 1 2y) 1 4(3x 2 6y)
48. 28(y 1 3t) 2 4(2y 2 t)
© Marshall Cavendish International (Singapore) Private Limited.
Expand and simplify each expression with two variables.
42 Chapter 3 Lesson 3.4
(M)MIFEP_C2A_Ch03.indd 42
20/06/12 12:12 PM
Name: Date: Write an expression for the missing dimension of each shaded figure
and a multiplication expression for its area. Then expand and simplify
the multiplication expression.
49.
12
(x 3)
?
14
50.
8
2x
?
© Marshall Cavendish International (Singapore) Private Limited.
16
Write an expression for the area of the figure. Expand and simplify.
51.
10
2x 3y
6y
Extra Practice Course 2A 43
(M)MIFEP_C2A_Ch03.indd 43
22/06/12 1:32 PM
1
1
(14k 2 10) 5 [14k 1 (210)]
2
2
1
1
5 (14k) 1 (210)
2
2
33. 3 x 1 x 1 y 5 y 4 x 4 y
7
6
6
3.
7
6
4
2
x y
7
3
34. 3 p 1 p 5 q 1 q 3 p 2 p 5 q 3 q
4
2
9
3
4
4
1
2
p q
4
9
35.
6.4m 1 2.3n 2 5.7m 2 0.7n
5 (6.4m 2 5.7m) 1 (2.3n 2 0.7n)
5 0.7m 1 1.6n
36.
6.9a 2 4.9b 2 7.8a 2 0.4b
5 (6.9a 2 7.8a) 1 (24.9b 2 0.4b)
5 20.9a 2 5.3b
37. 8 x 4 y 2 x 1 y
9
5
3
2
13
x y
9
10
4
1
8
3
5 7k 1 (25)
5 7k 2 5
1
[8a 1 (224)]
8
1
1
5 (8a) 1 (224)
8
8
4. (8a 2 24) 5
1
2
5 a 1 (23)
5a23
1
2
1
2
5. (4p 1 1) 5 (4p) 1 (1)
5 2p 1
1
2
1
1
1
(2a 1 5) 5 (2a) 1 (5)
7
7
7
5
2
5 a1
7
7
6.
1
5
1
5
1
1
5 (3b) 1 (22)
5
5
3
2
5 b1 2
5
5
7. (3b 2 2) 5 [3b 1 (22)]
38. 8 a 7 b 2 a 5 b
5
9
2
8
2   4
1 
 x x   y y 
9
3   5
2 
8
6   8
5 
 x x   y y 
9
9   10
10 


2
13
x  y 
 10 
9
9
8
3
5 b2
2
5
8
2   7
5 
 a a   b b 
5
3   4
8 
 14
24
10
5 
a a  b b 
 8
15
15
8 
8. (2k 2 15) 5 [2k 1 (215)]
 9 
14
a  b 
 8 
15
5 (2k) 1 (215)
5 k 1 (29)
5 k29
14
9
a b
15
8
39. Perimeter 5
2  4.6x 1 2  2.8x
5 9.2x 1 5.6x
5 14.8x units
3
5
2
2
40. Perimeter 5
2x x x
5 6x units
Lesson 3.4
1. 1 (8x 16) 1 (8x ) 1 (16)
4
4
2x 4
4
2. 1 (3p 12) 1 (3p ) 1 (12)
3
3
p 4
3
5
3
3
5
5
3
5
6
3
5
5
6
5
9.2(6x 1 0.1) 5
2(6x) 1 2(0.1)
5 12x 1 0.2
10.5(0.3y 1 2) 5
5(0.3y) 1 5(2)
5 1.5y 1 10
11.0.3(5x 1 3) 5
0.3(5x) 1 0.3(3)
5 1.5x 1 0.9
12.0.4(2h 1 7) 5
0.4(2h) 1 0.4(7)
5 0.8h 1 2.8
13.0.6(m 2 4) 5
0.6[m 1 (24)]
5 0.6(m) 1 0.6(24)
5 0.6m 1 (22.4)
5 0.6m 2 2.4
14.0.5(p 2 3) 5
0.5[p 1 (23)]
5 0.5(p) 1 0.5(23)
5 0.5p 1 (21.5)
5 0.5p 2 1.5
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7
104 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 104
02/07/12 9:05 PM
15.0.2(1.2d 1 0.3) 5
0.2(1.2d ) 1 0.2(0.3)
5 0.24d 1 0.06
16.1.5(0.4x 2 1.3) 5
1.5[0.4x 1 (21.3)]
5 1.5(0.4x) 1 1.5(21.3)
5 0.6x 1 (21.95)
5 0.6x 2 1.95
17. 23(x 1 2) 5
23(x) 1 (23)(2)
5 23x 1 (26)
5 23x 2 6
18. 25(2x 1 3) 5
25(2x) 1 (25)(3)
5 210x 1 (215)
5 210x 2 15
19. 22(3a 1 7b) 5
22(3a) 1 (22)(7b)
5 26a 1 (214b)
5 26a 2 14b
20. 27(4k 2 h) 5
27(4k) 1 (27)(2h)
5 228k 1 7h
1

1 
21. 6  p 3 6  p  1 (26)(3)
2

2 
5 23p 1 (218)
5 23p 2 18
 1
 1
1
1
22. 8x    (8x )  
 4
 4
4
3
1
2x  1
 
 3
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12
23. 23(4k 1 1.2) 5
23(4k) 1 (23)(1.2)
5 212k 1 (23.6)
5 212k 2 3.6
24. 24(0.3m 1 7) 5
24(0.3m) 1 (24)(7)
5 21.2m 1 (228)
5 21.2m 2 28
25. 25(q 2 0.6) 5
25(q) 1 (25)(20.6)
5 25q 1 3
26. 20.2(0.6y 2 2) 5
20.2(0.6y) 1 (20.2)(22)
5 20.12y 1 0.4
27.2(3y 1 2) 1 5 5
2(3y) 1 2(2) 1 5
5 6y 1 4 1 5
5 6y 1 9
28.4(3a 1 1) 2 2 5
4(3a) 1 4(1) 2 2
5 12a 1 4 2 2
5 12a 1 2
29.3(x 1 8) 1 5x 5
3(x) 1 3(8) 1 5x
5 3x 1 24 1 5x
5 (3x 1 5x) 1 24
5 8x 1 24
30.7(b 1 4) 2 3b 5
7(b) 1 7(4) 2 3b
5 7b 1 28 2 3b
5 (7b 2 3b) 1 28
5 4b 1 28

1 
1
31. 3  a 2 5 3  a  3(2) 5

4 
4
3
a65
4
3
a 11
4
 1
1 
1
1
32. 6  a 3 a 6  a  6(3) a
 2
 12 
 12
2
6
1
a (18) a
2
12
6
1 
 a a  (18)


12
2
1
1 
 a a  (18)


2
2
5 218
33.0.4(x 1 3) 1 0.8x 5
0.4(x) 1 0.4(3) 1 0.8x
5 0.4x 1 1.2 1 0.8x
5 (0.4x 1 0.8x) 1 1.2
5 1.2x 1 1.2
34.0.3(y 1 5) 2 0.1y 5
0.3(y) 1 0.3(5) 2 0.1y
5 0.3y 1 1.5 2 0.1y
5 (0.3y 2 0.1y) 1 1.5
5 0.2y 1 1.5
35. 23(5m 1 1) 2 m 5
23(5m) 1 (23)(1) 2 m
5 215m 1 (23) 2 m
5 (215m 2 m) 1 (23)
5 216m 1 (23)
5 216m 2 3
36.12 2 4(n 2 2) 5
12 1 (24)(n) 1 (24)(22)
5 12 1 (24n) 1 8
5 (12 1 8) 1 (24n)
5 20 1 (24n)
5 20 2 4n
37. 20.6(r 1 4) 1 2.5r 5
20.6(r) 1 (20.6)(4) 1 2.5r
5 20.6r 1 (22.4) 1 2.5r
5 (20.6r 1 2.5r) 1 (22.4)
5 1.9r 1 (22.4)
5 1.9r 2
­ 2.4
38. 2(1.4x 1 5) 1 1.7x 5
(21)(1.4x) 1 (21)(5)
1 1.7x
5 21.4x 1 (25) 1 1.7x
5 (21.4x 1 1.7x) 1 (25)
5 0.3x 1 (25)
5 0.3x 2 5
39.15y 1 4(8y 1 x) 5
15y 1 4(8y) 1 4(x)
5 15y 1 32y 1 4x
5 47y 1 4x
9a 1 7(2a) 1 7(2b)
40.9a 1 7(2a 2 b) 5
5 9a 1 14a 1 (27b)
5 23a 1 (27b)
5 23a 2 7b
Extra Practice Course 2A 105
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 105
02/07/12 9:05 PM
50. Length of missing dimension:
(16 2 2x) units
Area 5
1
 8  (16 2 2x)
2
5 4  (16 2 2x)
5 4(16) 1 (4)(22x)
5 64 1 (28x)
5 (64 2 8x) units2
51.Area 5 10(2x 2 3y) 1
1
 10  6y
2
5 10(2x) 1 10(23y) 1 30y
5 10(2x) 1 (230y) 1 30y
5 20x 2 30y 1 30y
5 20x units2
Lesson 3.5
1.3x 1 15 5
3(x) 1 3(5)
5 3(x 1 5)
2.8a 1 8 5
8(a) 1 8(1)
5 8(a 1 1)
3.4x 2 28 5
4x 1 (228)
5 4(x) 1 4(27)
5 4(x 2 7)
4.5x 2 15 5
5x 1 (215)
5 5(x) 1 5(23)
5 5(x 2 3)
5.6a 1 6b 5
6(a) 1 6(b)
5 6(a 1 b)
6.2x 1 10y 5
2(x) 1 2(5y)
5 2(x 1 5y)
7.21p 1 7q 5
7(3p) 1 7(q)
5 7(3p 1 q)
8.16w 1 80m 5
16(w) 1 16(5m)
5 16(w 1 5m)
9.3j 2 18k 5
3j 1 (218k)
5 3(j) 1 3(26k)
5 3(j 2 6k)
10.12t 2 48u 5
12t 1 (248u)
5 12(t) 1 12(24u)
5 12(t 2 4u)
11.25a 2 5p 5
25a 1 (25p)
5 5(5a) 1 5(2p)
5 5(5a 2 p)
12.8h 2 56f 5
8h 1 (256f )
5 8(h) 1 8(27f )
5 8(h 2 7f)
13.16x 2 10y 5
16x 1 (210y)
5 2(8x) 1 2(25y)
5 2(8x 2 5y)
14.24a 2 6b 5
24a 1 (26b)
5 6(4a) 1 6(2b)
5 6(4a 2 b)
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41.6g 1 8(v 2 g) 5
6g 1 8(v) 1 8(2g)
5 6g 1 8v 1 (28g)
5 [6g 1 (28g)] 1 8v
5 (6g 2 8g) 1 8v
5 22g 1 8v
42.12p 1 10(p 2 2q) 5
12p 1 10(p) 1 10(22q)
5 12p 1 10p 1 (220q)
5 22p 1 (220q)
5 22p 2 20q
43.7(2a 1 b) 1 2(3a 1 b)
5 7(2a) 1 7(b) 1 2(3a) 1 2(b)
5 14a 1 7b 1 6a 1 2b
5 (14a 1 6a) 1 (7b 1 2b)
5 20a 1 9b
44.4(2m 2 n) 1 8(3n 2 m)
5 4(2m) 1 4(2n) 1 8(3n) 1 8(2m)
5 8m 1 (24n) 1 24n 1 (28m)
5 [8m 1 (28m)] 1 [(24n) 1 24n]
5 (8m 2 8m) 1 (24n 1 24n)
5 20n
45.5(3d 1 e) 2 4(d 2 4e)
5 5(3d) 1 5(e) 1 (24)(d) 1 (24)(24e)
5 15d 1 5e 1 (24d) 1 16e
5 [15d 1 (24d)] 1 (5e 1 16e)
5 (15d 2 4d) 1 (5e 1 16e)
5 11d 1 21e
46.6(4q 2 p) 2 (2q 2 5p)
5 6(4q) 1 6(2p) 1 (21)(2q) 1 (21)(25p)
5 24q 1 (26p) 1 (22q) 1 5p
5 [24q 1 (22q)] 1 [(26p) 1 5p]
5 (24q 2 2q) 1 (26p 1 5p)
5 22q 2 p
47. 23(x 1 2y) 1 4(3x 2 6y)
5 23(x) 1 (23)(2y) 1 4(3x) 1 4(26y)
5 23x 1 (26y) 1 12x 1 (224y)
5 (23x 1 12x) 1 [(26y) 1 (224y)]
5 (23x 1 12x) 1 (26y 2 24y)
5 9x 1 (230y)
5 9x 2 30y
48. 28(y 1 3t) 2 4(2y 2 t)
5 28(y) 1 (28)(3t) 1 (24)(2y) 1 (24)(2t)
5 28y 1 (224t) 1 (28y) 1 4t
5 [28y 1 (28y)] 1 [(224t) 1 4t]
5 (28y 2 8y) 1 (224t 1 4t)
5 216y 2 20t
49. Length of missing dimension:
14 2 (x 2 3) 5
14 1 (21)(x) 1 (21)(23)
5 14 1 (2x) 1 3
5 (14 1 3) 1 (2x)
5 17 1 (2x)
5 (17 2 x) units
Area 5
12  (17 2 x)
5 12(17) 1 12(2x)
5 204 1 (212x)
5 (204 2 12x) units2
106 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 106
02/07/12 9:05 PM
Name: Date: Lesson 3.5 Factoring Algebraic Expressions
1. 3x 1 15
2.8a 1 8
3. 4x 2 28
4.5x 2 15
5. 6a 1 6b
6.2x 1 10y
7. 21p 1 7q
8.16w 1 80m
9. 3j 2 18k
10.12t 2 48u
11. 25a 2 5p
12.8h 2 56f
13. 16x 2 10y
14.24a 2 6b
15. 35c 2 15d
16.14y 2 30e
17. 23 2 p
18. 2y 2 8
19. 24d 2 5
20. 25y 2 16
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Factor each expression with two terms.
44 Chapter 3 Lesson 3.5
MIF_ExtraPractice C2_Ch03.indd 44
08/12/11 11:47 AM
Name: Date: Factor each expression with negative terms.
21. 22a 2 4
22. 23x 2 24
23. 27k 2 35
24. 29u 2 81
25. 22 2 6n
26. 24 2 12p
27. 224x 2 18y
28. 235m 2 20n
29. 228w 2 7q
30. 248y 2 16x
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Factor each expression with three terms.
31. 3x 1 3y 1 9
32.4a 1 2b 1 6
33. 15p 1 5q 1 10
34.18d 1 9e 1 12
35. 4s 2 8t 2 20
36.7a 2 14b 2 28
37. 16a 2 12b 2 6
38.33g 2 11h 2 66
39. 9 1 18m 2 12n
40. 35 2 5w 1 25k
Extra Practice Course 2A 45
(M)MIFEP_C2A_Ch03.indd 45
20/06/12 12:12 PM
50. Length of missing dimension:
(16 2 2x) units
Area 5
1
 8  (16 2 2x)
2
5 4  (16 2 2x)
5 4(16) 1 (4)(22x)
5 64 1 (28x)
5 (64 2 8x) units2
51.Area 5 10(2x 2 3y) 1
1
 10  6y
2
5 10(2x) 1 10(23y) 1 30y
5 10(2x) 1 (230y) 1 30y
5 20x 2 30y 1 30y
5 20x units2
Lesson 3.5
1.3x 1 15 5
3(x) 1 3(5)
5 3(x 1 5)
2.8a 1 8 5
8(a) 1 8(1)
5 8(a 1 1)
3.4x 2 28 5
4x 1 (228)
5 4(x) 1 4(27)
5 4(x 2 7)
4.5x 2 15 5
5x 1 (215)
5 5(x) 1 5(23)
5 5(x 2 3)
5.6a 1 6b 5
6(a) 1 6(b)
5 6(a 1 b)
6.2x 1 10y 5
2(x) 1 2(5y)
5 2(x 1 5y)
7.21p 1 7q 5
7(3p) 1 7(q)
5 7(3p 1 q)
8.16w 1 80m 5
16(w) 1 16(5m)
5 16(w 1 5m)
9.3j 2 18k 5
3j 1 (218k)
5 3(j) 1 3(26k)
5 3(j 2 6k)
10.12t 2 48u 5
12t 1 (248u)
5 12(t) 1 12(24u)
5 12(t 2 4u)
11.25a 2 5p 5
25a 1 (25p)
5 5(5a) 1 5(2p)
5 5(5a 2 p)
12.8h 2 56f 5
8h 1 (256f )
5 8(h) 1 8(27f )
5 8(h 2 7f)
13.16x 2 10y 5
16x 1 (210y)
5 2(8x) 1 2(25y)
5 2(8x 2 5y)
14.24a 2 6b 5
24a 1 (26b)
5 6(4a) 1 6(2b)
5 6(4a 2 b)
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41.6g 1 8(v 2 g) 5
6g 1 8(v) 1 8(2g)
5 6g 1 8v 1 (28g)
5 [6g 1 (28g)] 1 8v
5 (6g 2 8g) 1 8v
5 22g 1 8v
42.12p 1 10(p 2 2q) 5
12p 1 10(p) 1 10(22q)
5 12p 1 10p 1 (220q)
5 22p 1 (220q)
5 22p 2 20q
43.7(2a 1 b) 1 2(3a 1 b)
5 7(2a) 1 7(b) 1 2(3a) 1 2(b)
5 14a 1 7b 1 6a 1 2b
5 (14a 1 6a) 1 (7b 1 2b)
5 20a 1 9b
44.4(2m 2 n) 1 8(3n 2 m)
5 4(2m) 1 4(2n) 1 8(3n) 1 8(2m)
5 8m 1 (24n) 1 24n 1 (28m)
5 [8m 1 (28m)] 1 [(24n) 1 24n]
5 (8m 2 8m) 1 (24n 1 24n)
5 20n
45.5(3d 1 e) 2 4(d 2 4e)
5 5(3d) 1 5(e) 1 (24)(d) 1 (24)(24e)
5 15d 1 5e 1 (24d) 1 16e
5 [15d 1 (24d)] 1 (5e 1 16e)
5 (15d 2 4d) 1 (5e 1 16e)
5 11d 1 21e
46.6(4q 2 p) 2 (2q 2 5p)
5 6(4q) 1 6(2p) 1 (21)(2q) 1 (21)(25p)
5 24q 1 (26p) 1 (22q) 1 5p
5 [24q 1 (22q)] 1 [(26p) 1 5p]
5 (24q 2 2q) 1 (26p 1 5p)
5 22q 2 p
47. 23(x 1 2y) 1 4(3x 2 6y)
5 23(x) 1 (23)(2y) 1 4(3x) 1 4(26y)
5 23x 1 (26y) 1 12x 1 (224y)
5 (23x 1 12x) 1 [(26y) 1 (224y)]
5 (23x 1 12x) 1 (26y 2 24y)
5 9x 1 (230y)
5 9x 2 30y
48. 28(y 1 3t) 2 4(2y 2 t)
5 28(y) 1 (28)(3t) 1 (24)(2y) 1 (24)(2t)
5 28y 1 (224t) 1 (28y) 1 4t
5 [28y 1 (28y)] 1 [(224t) 1 4t]
5 (28y 2 8y) 1 (224t 1 4t)
5 216y 2 20t
49. Length of missing dimension:
14 2 (x 2 3) 5
14 1 (21)(x) 1 (21)(23)
5 14 1 (2x) 1 3
5 (14 1 3) 1 (2x)
5 17 1 (2x)
5 (17 2 x) units
Area 5
12  (17 2 x)
5 12(17) 1 12(2x)
5 204 1 (212x)
5 (204 2 12x) units2
106 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 106
02/07/12 9:05 PM
© Marshall Cavendish International (Singapore) Private Limited.
15.35c 2 15d 5
35c 1 (215d )
5 5(7c) 1 5(23d )
5 5(7c 2 3d )
16.14y 2 30e 5
14y 1 (230e)
5 2(7y) 1 2(215e)
5 2(7y 2 15e)
17. 23 2 p 5
23 1 (2p)
5 (21)(3) 1 (21)(p)
5 (21)(3 1 p)
5 2(3 1 p)
18. 2y 2 8 5
2y 1 (28)
5 (21)(y) 1 (21)(8)
5 (21)(y 1 8)
5 2(y 1 8)
19. 24d 2 5 5
24d 1 (25)
5 (21)(4d ) 1 (21)(5)
5 (21)(4d 1 5)
5 2(4d 1 5)
20. 25y 2 16 5
25y 1 (216)
5 (21)(5y) 1 (21)(16)
5 (21)(5y 1 16)
5 2(5y 1 16)
21. 22a 2 4 5
22a 1 (24)
5 (22)(a) 1 (22)(2)
5 22(a 1 2)
22. 23x 2 24 5
23x 1 (224)
5 (23)(x) 1 (23)(8)
5 23(x 1 8)
23. 27k 2 35 5
27k 1 (235)
5 (27)(k) 1 (27)(5)
5 27(k 1 5)
24. 29u 2 81 5
29u 1 (281)
5 (29)(u) 1 (29)(9)
5 29(u 1 9)
25. 22 2 6n 5
22 1 (26n)
5 (22)(1) 1 (22)(3n)
5 22(1 1 3n)
26. 24 2 12p 5
24 1 (212p)
5 (24)(1) 1 (24)(3p)
5 24(1 1 3p)
27. 224x 2 18y 5
224x 1 (218y)
5 (26)(4x) 1 (26)(3y)
5 26(4x 1 3y)
28. 235m 2 20n 5
235m 1 (220n)
5 (25)(7m) 1 (25)(4n)
5 25(7m 1 4n)
29. 228w 2 7q 5
228w 1 (27q)
5 (27)(4w) 1 (27)(q)
5 27(4w 1 q)
30. 248y 2 16x 5
248y 1 (216x)
5 (216)(3y) 1 (216)(x)
5 216(3y 1 x)
31.3x 1 3y 1 9 5
3(x) 1 3(y) 1 3(3)
5 3(x 1 y 1 3)
32.4a 1 2b 1 6 5
2(2a) 1 2(b) 1 2(3)
5 2(2a 1 b 1 3)
33.15p 1 5q 1 10 5
5(3p) 1 5(q) 1 5(2)
5 5(3p 1 q 1 2)
34.18d 1 9e 1 12 5
3(6d) 1 3(3e) 1 3(4)
5 3(6d 1 3e 1 4)
35.4s 2 8t 2 20 5
4s 1 (28t) 1 (220)
5 4(s) 1 4(22t) 1 4(25)
5 4[s 1 (22t) 1 (25)]
5 4(s 2 2t 2 5)
36.7a 2 14b 2 28 5
7a 1 (214b) 1 (228)
5 7(a) 1 7(22b) 1 7(24)
5 7[a 1 (22b) 1 (24)]
5 7(a 2 2b 2 4)
37.16a 2 12b 2 6 5
16a 1 (212b) 1 (26)
5 2(8a) 1 2(26b) 1 2(23)
5 2[8a 1 (26b) 1 (23)]
5 2(8a 2 6b 2 3)
38.33g 2 11h 2 66 5
33g 1 (211h) 1 (266)
5 11(3g) 1 11(2h) 1 11(26)
5 11[3g 1 (2h) 1 (26)]
5 11(3g 2 h 2 6)
39.9 1 18m 2 12n 5
9 1 18m 1 (212n)
5 3(3) 1 3(6m) 1 3(24n)
5 3[3 1 6m 1 (24n)]
5 3(3 1 6m 2 4n)
40.35 2 5w 1 25k 5
35 1 (25w) 1 25k
5 5(7) 1 5(2w) 1 5(5k)
5 5[7 1 (2w) 1 5k]
5 5(7 2 w 1 5k)
Lesson 3.6
1.
t
s
2
3
2. 15 b 20
23
3.
5r 7
35r
15
15
7r
3
4. 1.2  w  1.2 w 1.2 12
12
u
u
5 1.2w 1
5.
u
10
9
27
(6 x ) 10 x 10
14
7
6. 20 1 w 1 w
100 2
10
21p
7. 7 (5p 3) 10
2
Extra Practice Course 2A 107
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 107
02/07/12 9:05 PM
Name: Date: Lesson 3.6 Writing Algebraic Expressions
Translate each verbal description into an algebraic expression. Simplify
the expression when you can.
1. Sum of one-half t and one-third s
2. Twenty subtracted from
15
b
23
3. Product of 5r and 7 divided by 15
4. 120% of the sum of w and one-twelfth u
5. Nine-fourteenths of 6x reduced by 10
7. Seven-tenths of the product of 5p and 3
8. Sum of x, three-fourths x, and 90% of z
9. Four times the difference of one-half x subtracted from three-eighths y
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6. 20% of one-half w
10. 60% of the difference of five-eighteenths v subtracted from four-sixths w
46 Chapter 3 Lesson 3.6
(M)MIFEP_C2A_Ch03.indd 46
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Name: Date: Solve. You may use a diagram, model, or table.
3
11. The length of a picture frame is (8u 2 12) inches. Its width is of its length.
4
Express the width of the picture frame in terms of u.
12. If 6 tablespoons are equivalent to 1 fluid ounce, how many fluid ounces are
in (10t 2 4) tablespoons?
© Marshall Cavendish International (Singapore) Private Limited.
13. 11 notebooks were added to w notebooks. 7 friends then shared the
notebooks equally. Express the number of notebooks each person received
in terms of w.
14. A pear costs $0.40 and an apple costs $0.25. What is the total cost of
p pears and q apples?
15. The ratio of the number of pencils to pens is 5 : 7. There are q pens. Express
the number of pencils in terms of q.
Extra Practice Course 2A 47
(M)MIFEP_C2A_Ch03.indd 47
20/06/12 12:12 PM
Name: Date: 16. When 5 adults joined a group of y diners, the ratio of the number of adults
to children in the restaurant became 3 : 5. Express the number of children in
terms of y.
17. Freddy paid w dollars for a camera and $120 for an additional camera lens.
If the sales tax is 8%, how much did Freddy pay for the camera and lens,
including the sales tax?
18. Emily has 5u game cards. John has 8 fewer game cards than Emily. Find
13
19. A train traveled at 140 miles per hour for 2 1 x hours, and (2x 2 3) miles per
14
hour for the next 3 hours.
a) Express the total distance traveled by the train in terms of x.
b)If x 5 3, what is the total distance traveled by the train?
© Marshall Cavendish International (Singapore) Private Limited.
the average number of game cards that Emily and John have in all in terms
of u.
48 Chapter 3 Lesson 3.6
(M)MIFEP_C2A_Ch03.indd 48
20/06/12 12:12 PM
© Marshall Cavendish International (Singapore) Private Limited.
15.35c 2 15d 5
35c 1 (215d )
5 5(7c) 1 5(23d )
5 5(7c 2 3d )
16.14y 2 30e 5
14y 1 (230e)
5 2(7y) 1 2(215e)
5 2(7y 2 15e)
17. 23 2 p 5
23 1 (2p)
5 (21)(3) 1 (21)(p)
5 (21)(3 1 p)
5 2(3 1 p)
18. 2y 2 8 5
2y 1 (28)
5 (21)(y) 1 (21)(8)
5 (21)(y 1 8)
5 2(y 1 8)
19. 24d 2 5 5
24d 1 (25)
5 (21)(4d ) 1 (21)(5)
5 (21)(4d 1 5)
5 2(4d 1 5)
20. 25y 2 16 5
25y 1 (216)
5 (21)(5y) 1 (21)(16)
5 (21)(5y 1 16)
5 2(5y 1 16)
21. 22a 2 4 5
22a 1 (24)
5 (22)(a) 1 (22)(2)
5 22(a 1 2)
22. 23x 2 24 5
23x 1 (224)
5 (23)(x) 1 (23)(8)
5 23(x 1 8)
23. 27k 2 35 5
27k 1 (235)
5 (27)(k) 1 (27)(5)
5 27(k 1 5)
24. 29u 2 81 5
29u 1 (281)
5 (29)(u) 1 (29)(9)
5 29(u 1 9)
25. 22 2 6n 5
22 1 (26n)
5 (22)(1) 1 (22)(3n)
5 22(1 1 3n)
26. 24 2 12p 5
24 1 (212p)
5 (24)(1) 1 (24)(3p)
5 24(1 1 3p)
27. 224x 2 18y 5
224x 1 (218y)
5 (26)(4x) 1 (26)(3y)
5 26(4x 1 3y)
28. 235m 2 20n 5
235m 1 (220n)
5 (25)(7m) 1 (25)(4n)
5 25(7m 1 4n)
29. 228w 2 7q 5
228w 1 (27q)
5 (27)(4w) 1 (27)(q)
5 27(4w 1 q)
30. 248y 2 16x 5
248y 1 (216x)
5 (216)(3y) 1 (216)(x)
5 216(3y 1 x)
31.3x 1 3y 1 9 5
3(x) 1 3(y) 1 3(3)
5 3(x 1 y 1 3)
32.4a 1 2b 1 6 5
2(2a) 1 2(b) 1 2(3)
5 2(2a 1 b 1 3)
33.15p 1 5q 1 10 5
5(3p) 1 5(q) 1 5(2)
5 5(3p 1 q 1 2)
34.18d 1 9e 1 12 5
3(6d) 1 3(3e) 1 3(4)
5 3(6d 1 3e 1 4)
35.4s 2 8t 2 20 5
4s 1 (28t) 1 (220)
5 4(s) 1 4(22t) 1 4(25)
5 4[s 1 (22t) 1 (25)]
5 4(s 2 2t 2 5)
36.7a 2 14b 2 28 5
7a 1 (214b) 1 (228)
5 7(a) 1 7(22b) 1 7(24)
5 7[a 1 (22b) 1 (24)]
5 7(a 2 2b 2 4)
37.16a 2 12b 2 6 5
16a 1 (212b) 1 (26)
5 2(8a) 1 2(26b) 1 2(23)
5 2[8a 1 (26b) 1 (23)]
5 2(8a 2 6b 2 3)
38.33g 2 11h 2 66 5
33g 1 (211h) 1 (266)
5 11(3g) 1 11(2h) 1 11(26)
5 11[3g 1 (2h) 1 (26)]
5 11(3g 2 h 2 6)
39.9 1 18m 2 12n 5
9 1 18m 1 (212n)
5 3(3) 1 3(6m) 1 3(24n)
5 3[3 1 6m 1 (24n)]
5 3(3 1 6m 2 4n)
40.35 2 5w 1 25k 5
35 1 (25w) 1 25k
5 5(7) 1 5(2w) 1 5(5k)
5 5[7 1 (2w) 1 5k]
5 5(7 2 w 1 5k)
Lesson 3.6
1.
t
s
2
3
2. 15 b 20
23
3.
5r 7
35r
15
15
7r
3
4. 1.2  w  1.2 w 1.2 12
12
u
u
5 1.2w 1
5.
u
10
9
27
(6 x ) 10 x 10
14
7
6. 20 1 w 1 w
100 2
10
21p
7. 7 (5p 3) 10
2
Extra Practice Course 2A 107
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 107
02/07/12 9:05 PM
7
x 0.9z
4
3 
 1 
3
1 
9. 4  y x  4  y  4  x 
8 
 2 
8
2 
3
y (2x )
2
3
y 2x
2
10. 60  4 w 5 v  60  4 w  60  5 v 
100  6
18 
100  6 
100  18 
 1 
2
w  v 
 6 
5
2
17. Cost of camera and lens before tax:
w 1 120 dollars
Cost of camera and lens including tax:
1.08(w 1 120) 5 1.08  w 1 1.08  120
5 (1.08w 1 129.6) dollars
Freddy paid (1.08w 1 129.6) dollars for the
camera and lens.

8
18. Number of cards John has: 5u 

13 
1
w v
5
6
Total number of cards that Emily and
John have: 5u 2
8
8
1 5u 5 (5u 1 5u) 2
13
13
8
5 10u 2
13
Average number of cards:
1
8
1
1 8 
10u  (10u )  
2
13 
2
2  13 
 4
5u  
 13 
3
3
3
11.Width: (8u 2 12) 5 (8u) 1 (212)
4
4
4
5 6u 1 (29)
5 (6u 2 9) in.
The width of the picture frame is
(6u 2 9) inches.
Emily and John have an average of

4
5u  game cards.

13 
1
6
1
(10t 2 4) tablespoons 5 (10t 2 4) fl oz
6
1
1
5  10t 2  4
6
6
12. 1 tablespoon 5 fl oz
5
2
 t  fl oz
3
3
5
2
 t  fluid ounces are in (10t 2 4)
3
3
tablespoons.
 11 w 
13. Each person received  7  notebooks.


14. The total cost of p pears and p apples is
0.4p 1 0.25q.
5
15. Number of pencils: q
7
5
There are q pencils.
7
16. Number of diners after 5 adults joined: y 1 5
5
8
Number of children: ( y 5)
The number of children is ( y 5) .
5
8
5u 4
13
19.a) Total distance traveled:
140  2
1
x 1 3(2x 2 3)
14
5 140  29
x 1 3(2x) 1 3(23)
14
5 290x 1 6x 1 (29)
5 290x 1 6x 2 9
5 (296x 2 9) mi
The total distance traveled by the train
is (296x 2 9) miles.
b)When x 5 3, total distance traveled:
296x 2 9 5 296  3 2 9 5 879 mi
The total distance traveled by the train
is 879 miles.
Lesson 3.7
1. Difference in length:
(12.5x 1 17) 2 (5x 1 0.4w)
5 12.5x 1 17 1 (21)(5x) 1 (21)(0.4w)
5 12.5x 1 (21)(5x) 1 17 1 (21)(0.4w)
5 12.5x 2 5x 1 17 2 0.4w
5 (7.5x 1 17 2 0.4w) cm
The difference in the length of the two ropes is
(7.5x 1 17 2 0.4w) centimeters.
© Marshall Cavendish International (Singapore) Private Limited.
3
4
3
8. x x 0.9z  x x  0.9z
4
4
4 
108 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 108
02/07/12 9:05 PM
Name: Date: Lesson 3.7 Real-World Problems: Algebraic Reasoning
Solve each question using algebraic reasoning.
1. Jeremy has two ropes. The longer rope is (12.5x 1 17) centimeters long,
and the shorter rope is (5x 1 0.4w) centimeters long. Find the difference in
length of the two ropes.
2. The radius of a circle is (7n 2 21) inches. Find the circumference of the circle
in terms of n. Use 22 as an approximation for π.
7
© Marshall Cavendish International (Singapore) Private Limited.
3. The average daily sales at a bookstore was (7.6k 1 2.2) dollars over a 4-day
promotion. Find the total sales during the promotion.
4. The ratio of the number of red ribbons to yellow ribbons is 17 to 6. If the
number of red ribbons is 2m 1 5, how many ribbons are yellow?
5. During summer vacation, 36% of c children went to Europe, 24 children to
Asia, and the rest of the children went to South America. How many
children went to South America?
Extra Practice Course 2A 49
(M)MIFEP_C2A_Ch03.indd 49
20/06/12 12:12 PM
Name: Date: 6. The hourly rates for a parking garage are as follows:
First hour
$4.00
Each additional hour thereafter
$3.20
Robyn parked her car in the garage for y hours. How much was her
parking fee?
7. A cylinder contains (4.5x 1 2y 2 6) milliliters of liquid. How many milliliters
of liquid must be added to the cylinder to make a total of (6.9x 2 3y 1 3)
milliliters?
8. Among the 50 children at a book fair, b of them are boys. 30% of the girls
at the book fair are younger than twelve years old while 40% of the boys are
at least twelve years old. How many children at the book fair are younger
than twelve years old?
9. When 2 of the koi was given away, there were still b koi and k goldfish left in
5
10. The ratio of the mass of Bottle A to Bottle B to Bottle C is 7 : 5 : 11. The
total mass of Bottle A and Bottle C is (2x 2 9) kilograms.
a) Express the mass of Bottle B in terms of x.
b)If x 5 15, find the mass of Bottle B.
© Marshall Cavendish International (Singapore) Private Limited.
the pond. How many koi and goldfish were there initially?
50 Chapter 3 Lesson 3.7
(M)MIFEP_C2A_Ch03.indd 50
20/06/12 12:12 PM
7
x 0.9z
4
3 
 1 
3
1 
9. 4  y x  4  y  4  x 
8 
 2 
8
2 
3
y (2x )
2
3
y 2x
2
10. 60  4 w 5 v  60  4 w  60  5 v 
100  6
18 
100  6 
100  18 
 1 
2
w  v 
 6 
5
2
17. Cost of camera and lens before tax:
w 1 120 dollars
Cost of camera and lens including tax:
1.08(w 1 120) 5 1.08  w 1 1.08  120
5 (1.08w 1 129.6) dollars
Freddy paid (1.08w 1 129.6) dollars for the
camera and lens.

8
18. Number of cards John has: 5u 

13 
1
w v
5
6
Total number of cards that Emily and
John have: 5u 2
8
8
1 5u 5 (5u 1 5u) 2
13
13
8
5 10u 2
13
Average number of cards:
1
8
1
1 8 
10u  (10u )  
2
13 
2
2  13 
 4
5u  
 13 
3
3
3
11.Width: (8u 2 12) 5 (8u) 1 (212)
4
4
4
5 6u 1 (29)
5 (6u 2 9) in.
The width of the picture frame is
(6u 2 9) inches.
Emily and John have an average of

4
5u  game cards.

13 
1
6
1
(10t 2 4) tablespoons 5 (10t 2 4) fl oz
6
1
1
5  10t 2  4
6
6
12. 1 tablespoon 5 fl oz
5
2
 t  fl oz
3
3
5
2
 t  fluid ounces are in (10t 2 4)
3
3
tablespoons.
 11 w 
13. Each person received  7  notebooks.


14. The total cost of p pears and p apples is
0.4p 1 0.25q.
5
15. Number of pencils: q
7
5
There are q pencils.
7
16. Number of diners after 5 adults joined: y 1 5
5
8
Number of children: ( y 5)
The number of children is ( y 5) .
5
8
5u 4
13
19.a) Total distance traveled:
140  2
1
x 1 3(2x 2 3)
14
5 140  29
x 1 3(2x) 1 3(23)
14
5 290x 1 6x 1 (29)
5 290x 1 6x 2 9
5 (296x 2 9) mi
The total distance traveled by the train
is (296x 2 9) miles.
b)When x 5 3, total distance traveled:
296x 2 9 5 296  3 2 9 5 879 mi
The total distance traveled by the train
is 879 miles.
Lesson 3.7
1. Difference in length:
(12.5x 1 17) 2 (5x 1 0.4w)
5 12.5x 1 17 1 (21)(5x) 1 (21)(0.4w)
5 12.5x 1 (21)(5x) 1 17 1 (21)(0.4w)
5 12.5x 2 5x 1 17 2 0.4w
5 (7.5x 1 17 2 0.4w) cm
The difference in the length of the two ropes is
(7.5x 1 17 2 0.4w) centimeters.
© Marshall Cavendish International (Singapore) Private Limited.
3
4
3
8. x x 0.9z  x x  0.9z
4
4
4 
108 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 108
02/07/12 9:05 PM
2.Circumference 5 2 r
 22 
2   (7n 21)
7
 44 
  (7n 21)
7
 44 
 44 
  (7n )   (21)
7
7
44n (132)
( 44n 132) in.
The circumference of the circle is
(44n 2 132) inches.
3.Total sales: 4
(7.6k 1 2.2)
5 4(7.6k) 1 4(2.2)
5 (30.4k 1 8.8) dollars
The total sales during the promotion was
(30.4k 1 8.8) dollars.
4.Number of yellow ribbons:
© Marshall Cavendish International (Singapore) Private Limited.
There are
6
17
12
17
(2m) 6
17
13
m 1
17
( 5) 6
17
6
17
12
17
(2m 5)
(2m) 6
17
13
( 5)
m 1
8.Number of girls: 50 2 b
Number of girls younger than 12 years old:
0.3(50 2 b) 5
0.3(50) 1 0.3(2b)
5 15 2 0.3b
Number of boys younger than 12 years old:
(1 2 0.4)b 5 0.6b
Number of children younger than 12 years old:
(15 2 0.3b) 1 0.6b 5
15 2 0.3b 1 0.6b
5 15 1 0.3b
(15 1 0.3b) children are younger than
3
12 years old.
b
3
53
9.Number of koi initially: bb
353
5
bb
53
533
Number of fish initially: bbb k
355
3
5
b
b
 5
3533
There were  bbb
kk koi and goldfish initially.

5355
b
5
5
10.a) Mass of Bottle B: (2x 9) kg
17
18
b)When x 5 15, mass of Bottle B:
5
18
(2 x 9 ) yellow ribbons.
5.Number of children who went to South
America: c 2 0.36c 2 24
5 0.64c 2 24
(0.64c 2 24) children went to South America.
6.Parking fee: 4
(1) 1 3.2(y 2 1)
5 4 1 3.2y 1 3.2(21)
5 4 1 3.2(21) + 3.2y
5 4 2 3.2 1 3.2y
5 (0.8 1 3.2y) dollars
Her parking fee was (0.8 1 3.2y) dollars.
7.Additional amount of liquid required:
5 (6.9x 2 3y 1 3) 2 (4.5x 1 2y 2 6)
5 6.9x 2 3y 1 3 1 (21)(4.5x) 1 (21)(2y) 1
(21)(26)
5 6.9x 1 (21)(4.5x) 2 3y 1 (21)(2y) 1 3 1
(21)(26)
5 6.9x 2 4.5x 2 3y 2 2y 1 3 1 6
5 (2.4x 2 5y 1 9) mL
(2.4x 2 5y 1 9) milliliters of liquid must be
added.
5
18
5
18
5
18
35
6
(2 15 9)
(30 9)
(21)
kg
The mass of Bottle B when x 5 15
is
35
6
kilograms.
Brain@Work
1.Second number:
5 52 2
 
x x 12
12
 3 3
 
16 16
5 2 
5
)
5 x2 x (5(12
16 163 3  1616 12)
5
 15 15 
x5 
24 24 x   4 4
5
15
15
x5 24 x 4
24
4
8 5 
8  15 
First number:
 x    3
5 24
5
4
1
 65 3 8  15 
x8
3 5  24 x  5  4  3
1
3
x1 9
x 63
3
1
x 9
3
Extra Practice Course 2A 109
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 109
02/07/12 9:05 PM
Name: Date: Lesson 4.2 Solving Algebraic Equations
© Marshall Cavendish International (Singapore) Private Limited.
Solve each equation with variables on the same side.
1. 5x 1 3 5 7
2.4y 2 7 5 5
3. 9p 1 5 5 213
4.23 5 6x 2 1
5.
2
x 5 1
3
6.
7
y 31
5
5
7.
5
p 9 3 8
4 8
8.
5 3
2
x
6 4
3
9. 5.7 1 0.3y 5 6.9
10.4.2 1 2.5a 5 9.2
11. 3.2y 2 7 5 9
12.5.5p 2 6.8 5 15.2
13. 3.8x 1 5.2x 2 6.7 5 11.3
14.7.8y 2 4.9 2 5.4y 5 2.3
Extra Practice Course 2A 53
(M)MIFEP_C2A_Ch04.indd 53
20/06/12 12:10 PM
Name: Date: Solve each equation with variables on both sides.
15. 5a 1 3 5 2a 1 9
16.21b 1 9 5 15b 1 3
17. 5x 2 11 5 12x 1 10
18.9y 2 5 5 15y 2 17
19.
4
2
p 4 p 5
3
20. 11 m 1 m 2m
21.
1
1
5
3
a a 3
4
6
2
3
1
1
22. 5 m 4 m 4
24.13.7b 2 3 5 3 2 4.3b
© Marshall Cavendish International (Singapore) Private Limited.
23. 2a 2 9.3 5 0.8a 1 5.1
4
54 Chapter 4 Lesson 4.2
MIF_ExtraPractice C2_Ch04.indd 54
08/12/11 11:48 AM
Name: Date: Solve each equation involving parentheses.
25. 4(3x 2 2) 5 16
26.24y 5 8(12 2y)
27. 3(4x 2 1) 2 7x 5 17
28.5(2 2 3y) 2 9y 5 4(3 2 2y)
29.
3
3
(5a 3) 4
8
2
1
30.
13
© Marshall Cavendish International (Singapore) Private Limited.
31. 5 x 4 ( x 8) 2
4
1
(m 1) m 1
5
5
32.6(3.2y 2 1) 5 3.6
33. 1.8(5a 1 3) 1 5.6 5 29
34.0.4(2x 2 3) 5 0.2x
35. 0.5(2m 2 3) 2 0.8m 5 2.7
36.0.8(4p 1 5) 5 4(0.5p 2 2)
Extra Practice Course 2A 55
MIF_ExtraPractice C2_Ch04.indd 55
08/12/11 11:48 AM
Then check to see if 10 is the solution of the
© Marshall Cavendish International (Singapore) Private Limited.
2
equation x 2 3 5 1.
5
2
2
If x 5 10, x 2 3 5  10 2 3
5
5
5423
51
Because the equations have same solution,
they are equivalent equations.
10. 23x 1 4 5 1 and x 5 21
If x 5 21, 23x 1 4 5
23  (21) 1 4
5 7 ( 1)
Because the equations have different
solutions, they are not equivalent equations.
11. 8x 5 16
8x 4 8 5 16 4 8
x52
So, 8x 5 16 and b) are equivalent equations.
12. x1356
x13235623
x 5 3
x  2 5 3  2
2x 5 6
So, x 1 3 5 6 and c) are equivalent
equations.
13. 2x 1 13 5 9
2x 1 13 2 13 5 9 2 13
2x 5 24
2x 4 2 5 24 4 2
x 5 22
1 1 x 5 1 1 (22)
1 1 x 5 21
So, 2x 1 13 5 9 and e) are equivalent
equations.
14. 4 2 5x 5 21
4 2 5x 2 4 5 21 2 4
25x 5 25
25x 4 (25) 5 25 4 (25)
x51
So, 4 2 5x 5 21 and a) are equivalent
equations.
15. 1
x 2 2 5 0
3
1
x 2 2 1 2 5 0 1 2
3
1
x 5 2
3
1
x  9 5 2  9
3
3x 5 18
3x 2 4 5 18 2 4
3x 2 4 5 14
Lesson 4.2
1. 5x 1 3
5x 1 3 2 3
5x
5x 4 5
5
5
5
5
x 5
7
723
4
445
4
5
2. 4y 2 7 5 5
4y 2 7 1 7 5 5 1 7
4y 5 12
4y 4 4 5 12 4 4
y53
3. 9p 1 5 5 213
9p 1 5 2 5 5 213 2 5
9p 5 218
9p 4 9 5 218 4 9
p 5 22
4. 23 5 6x 2 1
23 1 1 5 6x 2 1 1 1
24 5 6x
24 4 6 5 6x 4 6
4 5 x
2
3
5. x 2 5 5 1
2
x 2 5 1 5 5 1 1 5
3
2
x 5 6
3
2
2
2
x 4 5 6 4
3
3
3
3
x56
2
x59
7
1
5
5
7
1
15
y 5
2
5
5
5
7
14
y 5
5
5
6. y 5 3 2
7y 5 14
y 5 14 4 7
y 5 2
5
9
3
8
4
8
5
18
3
p
8
8
8
5
15
p
8
8
7. p 5p 5 15
5p 4 5 5 15 4 5
p53
1
3
So, x 2 2 5 0 and d) are equivalent
equations.
Extra Practice Course 2A 111
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 111
02/07/12 9:05 PM
9
3
x
6
4
9
3
3
3
x
6
4
4
4
9 4
x
6 3
2 5 x
9. 5.7 1 0.3y 5 6.9
5.7 1 0.3y 2 5.7 5 6.9 2 5.7
0.3y 5 1.2
0.3y 4 0.3 5 1.2 4 0.3
y54
10. 4.2 1 2.5a 5 9.2
4.2 1 2.5a 2 4.2 5 9.2 2 4.2
2.5a 5 5
2.5a 4 2.5 5 5 4 2.5
a52
11. 3.2y 2 7 5 9
3.2y 2 7 1 7 5 9 1 7
3.2y 5 16
3.2y 4 3.2 5 16 4 3.2
y 5 5
12. 5.5p 2 6.8 5 15.2
5.5p 2 6.8 1 6.8 5 15.2 1 6.8
5.5p 5 22
5.5p 4 5.5 5 22 4 5.5
p54
13.3.8x 1 5.2x 2 6.7 5 11.3
9x 2 6.7 5 11.3
9x 2 6.7 1 6.7 5 11.3 1 6.7
9x 5 18
9x 4 9 5 18 4 9
x52
14.7.8y 2 4.9 2 5.4y 5 2.3
7.8y 2 5.4y 2 4.9 5 2.3
2.4y 2 4.9 5 2.3
2.4y 2 4.9 1 4.9 5 2.3 1 4.9
2.4y 5 7.2
2.4y 4 2.4 5 7.2 4 2.4
y 5 3
15. 5a 1 3 5 2a 1 9
5a 1 3 2 2a 5 2a 1 9 2 2a
3a 1 3 5 9
3a 1 3 2 3 5 9 2 3
3a 5 6
3a 4 3 5 6 4 3
a52
16. 21b 1 9 5 15b 1 3
21b 1 9 2 15b 5 15b 1 3 2 15b
6b 1 9 5 3
6b 1 9 2 9 5 3 2 9
6b 5 26
6b 4 6 5 26 4 6
b 5 21
17. 5x 2 11 5 12x 1 10
5x 2 11 2 5x 5 12x 1 10 2 5x
211 5 7x 1 10
211 2 10 5 7x 1 10 2 10
221 5 7x
221 4 7 5 7x 4 7
23 5 x
18.
9y 2 5 5 15y 2 17
9y 2 5 2 9y 5 15y 2 17 2 9y
25 5 6y 2 17
25 1 17 5 6y 2 17 1 17
12 5 6y
12 4 6 5 6y 4 6
25y
4
2
p4 p
5
3
4
2
2
2
p 4 p p p
5
3
3
3
19. 12
10
p p4 0
15
15
2
p40
15
2
p24145014
15
2
p 4
15
2
2
2
p
4
15
15
15
15
p 5 4 
2
p 5 30
20.
11 1 m 5
11 1 m 5
11 1 m 5
11 1 m 2 m 5
11 5
11 5
1
m 2 2m
4
1
8
m2 m
4
4
7
2 m
4
7
2 m2m
4
7
4
2 m2 m
4
4
11
2 m
4
© Marshall Cavendish International (Singapore) Private Limited.
5
3
2
x
6
4
3
5 2 3x 2 2
6
3
4
3 3
5
4
3
x
4
6 6
8.  11
 11
11
11 4   5 2 m 4  
 4
4
 4
11  2
4
5m
11
24 5 m
112 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 112
02/07/12 9:05 PM
1
1
5
3
a
3
4
6
2
1
1
1
5
3
1
a a a a
3
4
3
6
2
3
1
5
2
3
a a
6
6
2
4
1
3
3
a
6
2
4
1 3
1
3
3
a 2
2
2
4 2
1
6
1
a
4
4
2
5
1
a
2
4
5
1
1
1
a
2
2
4 2
5
 2 5 a
4
5 a
2
3
1
1
22. m 1 5 m 2
5
4
4
3
3
3
1
1
m1 2 m5m2 2 m
5
5
5
4
4
1 2 m 1
4
5
4
1 1
2
1
1
m 4 4
5
4
4
2
2
m
4
5
1
2
2 m 2
2
5
5
5
1
5
m
2 2
5 m
4
© Marshall Cavendish International (Singapore) Private Limited.
21. a 23. 2a 2 9.3 5 0.8a 1 5.1
2a 2 9.3 2 0.8a 5 0.8a 1 5.1 2 0.8a
1.2a 2 9.3 5 5.1
1.2a 2 9.3 1 9.3 5 5.1 1 9.3
1.2a 5 14.4
1.2a 4 1.2 5 14.4 4 1.2
a 5 12
24. 13.7b 2 3 5 3 2 4.3b
13.7b 2 3 1 4.3b 5 3 2 4.3b 1 4.3b
18b 2 3 5 3
18b 2 3 1 3 5 3 1 3
18b 5 6
18b 4 18 5 6 4 18
1
b
25. 4(3x 2 2) 5 16
1
1
 4(3x 2 2) 5  16
4
4
3x 2 2 5 4
3x 2 2 1 2 5 4 1 2
3x 5 6
3x 4 3 5 6 4 3
x52
26. 24y 5 8(12 2y)
1
1
 24y 5  8(12 2y)
8
8
3y
3y 1 2y
5y
5y 4 5
5
5
5
5
y 1 2 2y
1 2 2y 1 2y
1
145
1
5
27. 3(4x 2 1) 27x 5 17
3  4x 2 3  1 2 7x 5 17
12x 2 3 2 7x 5 17
5x 2 3 5 17
5x 2 3 1 3 5 17 1 3
5x 5 20
5x 4 5 5 20 4 5
x 5 4
28. 5(2 2 3y) 2 9y 5 4(3 2 2y)
5  2 2 5  3y 2 9y 5 4  3 2 4  2y
10 2 15y 2 9y 5 12 2 8y
10 2 24y 5 12 2 8y
10 2 24y 1 24y 5 12 2 8y 1 24y
10 5 12 1 16y
10 2 12 5 12 1 16y 2 12
22 5 16y
22 4 16 5 16y 4 16
1 y
8
3
3
29. (5a 2 3) 5
4
8
3
3
8  (5a 2 3) 5 8 
4
8
6(5a 2 3)
6  5a 2 6  3
30a 2 18
30a 2 18 1 18
30a
30a 4 30
5
5
5
5
5
5
a
3
3
3
3 1 18
21
21 4 30
7
10
3
Extra Practice Course 2A 113
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 113
02/07/12 9:05 PM
4(m 2 1) 2 m
4  m 2 4  1 2 m
4m 2 4 2 m
3m 2 4
3m 2 4 1 4
3m
3m 4 3
m
5
5
5
5
5
5
5
5
5
5
5
5
514
9
943
3
2
1
13
31. x (x 2 8) 5
5
4
2
2

13
1
20   x ( x 8) 5 20 
2
5

4
20 
2
1
x 2 20  (x 2 8) 5 130
5
4
8x 2 5(x 2 8) 5 130
8x 2 5  x 2 5  (28) 5 130
8x 2 5x 1 40 5 130
3x 1 40 5 130
3x 1 40 2 40 5 130 2 40
3x 5 90
3x 4 3 5 90 4 3
x 5 30
32. 6(3.2y 2 1) 5 3.6
6  3.2y 2 6  1 5 3.6
19.2y 2 6 5 3.6
19.2y 2 6 1 6 5 3.6 1 6
19.2y 5 9.6
19.2y 4 19.2 5 9.6 4 19.2
y 5 0.5
33. 1.8(5a 1 3) 1 5.6 5 29
1.8  5a 1 1.8  3 1 5.6 5 29
9a 1 5.4 1 5.6 5 29
9a 1 11 5 29
9a 1 11 2 11 5 29 2 11
9a 5 18
9a 4 9 5 18 4 9
a52
34. 0.4(2x 2 3) 5 0.2x
0.4  2x 2 0.4  3 5 0.2x
0.8x 2 1.2 5 0.2x
0.8x 2 1.2 2 0.2x 5 0.2x 2 0.2x
0.6x 2 1.2 5 0
0.6x 2 1.2 1 1.2 5 0 1 1.2
0.6x 5 1.2
0.6x 4 0.6 5 1.2 4 0.6
x52
35. 0.5(2m 2 3) 2 0.8m 5 2.7
0.5  2m 2 0.5  3 2 0.8m 5 2.7
m 2 1.5 2 0.8m 5 2.7
0.2m 2 1.5 5 2.7
0.2m 2 1.5 1 1.5 5 2.7 1 1.5
0.2m 5 4.2
0.2m 4 0.2 5 4.2 4 0.2
m 5 21
36. 0.8(4p 1 5) 5 4(0.5p 2 2)
0.8  4p 1 0.8  5 5 4  0.5p 2 4  2
3.2p 1 4 5 2p 2 8
3.2p 1 4 22p 5 2p 2 8 2 2p
1.2p 1 4 5 28
1.2p 1 4 2 4 5 28 2 4
1.2p 5 212
1.2p 4 1.2 5 212 4 1.2
p 5 210
Lesson 4.3
1.Let x represent the amount of money, in
dollars, Amy had initially.
Because Amy had $139 after Sam gave her
$27,
x 1 27 5 139
x 1 27 2 27 5 139 2 27
x 5 112
Amy had $112 initially.
2. Let the two facing page numbers be
x and (x 1 1).
Because the sum of the two facing page
numbers is 145,
x 1 (x 1 1) 5 145
x 1 x 1 1 5 145
2x 1 1 5 145
2x 1 1 2 1 5 145 2 1
2x 5 144
2x 4 2 5 144 4 2
x 5 72
If x 5 72, x 1 1 5 72 1 1
5 73
The two page numbers are 72 and 73.
© Marshall Cavendish International (Singapore) Private Limited.
4
1
m51
5
5
4
1 
5   (m 1) m 5 5  1
5
5 
4
1
5  (m 2 1) 2 5  m 5 5
5
5
30. (m 2 1) 2
114 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 114
02/07/12 9:05 PM
Name: Date: Lesson 4.3 Real-World Problems: Algebraic Equations
Solve. Show your work.
1. Amy had x dollars. After Sam gave her $27, she had $139. How much money
did she have initially?
2. The sum of two facing page numbers in a book is 145. What are the two
page numbers?
3. Jackson’s age was
2
of the age he will be 20 years from now 7 years ago.
5
How old is Jackson now?
5. Adrianne is planning to bake some chocolate, strawberry, and raisin muffins
for a party. She was asked to bake half as many chocolate muffins as raisin
muffins and three times as many strawberry muffins as chocolate muffins.
If she only had enough ingredients to bake 480 muffins, how many raisin
muffins did she bake?
© Marshall Cavendish International (Singapore) Private Limited.
4. The perimeter of an isosceles triangle is 32.7 inches. If the length of its base
is 9.5 inches, find the length of each of the other two sides.
56 Chapter 4 Lesson 4.3
(M)MIFEP_C2A_Ch04.indd 56
20/06/12 12:10 PM
Name: Date: 6. Mr. Sidney rented a car for a day. The rental fee consists of a flat rate of
$19.99 plus $0.21 per additional mile. For how many miles did Mr. Sidney
drive the car if he paid $52.54 for the car rental?
7. A food manufacturer donates money to schools based on the number of
its product labels the school collects. The students at one school collected
2,100 product labels in three months. The number of labels collected in the
first two months was three times the number of labels collected in the third
month. How many product labels were collected in the third month?
8. Find the length of the sides of triangle ABC if its perimeter is 33 inches.
B
2x in.
2(x 3) in.
A
© Marshall Cavendish International (Singapore) Private Limited.
C
3(x 2) in.
9. On a 3-week vacation to Paris, Martha’s expenses on food, gifts, and
accommodations was $80 less than three times her airfare. If the total
expenses for the trip was $2,660, how much was her airfare?
10. Mark cycles from home to school at a speed of 16 kilometers per hour. He
cycles back on the same route at a speed of 15 kilometers per hour. The
total time taken for the journey is 7 3 hours. Given that the distance from
4
his home to school is d kilometers, and that distance 5 speed  time, write
and solve an equation to find the total distance traveled by him.
Extra Practice Course 2A 57
(M)MIFEP_C2A_Ch04.indd 57
20/06/12 12:11 PM
4(m 2 1) 2 m
4  m 2 4  1 2 m
4m 2 4 2 m
3m 2 4
3m 2 4 1 4
3m
3m 4 3
m
5
5
5
5
5
5
5
5
5
5
5
5
514
9
943
3
2
1
13
31. x (x 2 8) 5
5
4
2
2

13
1
20   x ( x 8) 5 20 
2
5

4
20 
2
1
x 2 20  (x 2 8) 5 130
5
4
8x 2 5(x 2 8) 5 130
8x 2 5  x 2 5  (28) 5 130
8x 2 5x 1 40 5 130
3x 1 40 5 130
3x 1 40 2 40 5 130 2 40
3x 5 90
3x 4 3 5 90 4 3
x 5 30
32. 6(3.2y 2 1) 5 3.6
6  3.2y 2 6  1 5 3.6
19.2y 2 6 5 3.6
19.2y 2 6 1 6 5 3.6 1 6
19.2y 5 9.6
19.2y 4 19.2 5 9.6 4 19.2
y 5 0.5
33. 1.8(5a 1 3) 1 5.6 5 29
1.8  5a 1 1.8  3 1 5.6 5 29
9a 1 5.4 1 5.6 5 29
9a 1 11 5 29
9a 1 11 2 11 5 29 2 11
9a 5 18
9a 4 9 5 18 4 9
a52
34. 0.4(2x 2 3) 5 0.2x
0.4  2x 2 0.4  3 5 0.2x
0.8x 2 1.2 5 0.2x
0.8x 2 1.2 2 0.2x 5 0.2x 2 0.2x
0.6x 2 1.2 5 0
0.6x 2 1.2 1 1.2 5 0 1 1.2
0.6x 5 1.2
0.6x 4 0.6 5 1.2 4 0.6
x52
35. 0.5(2m 2 3) 2 0.8m 5 2.7
0.5  2m 2 0.5  3 2 0.8m 5 2.7
m 2 1.5 2 0.8m 5 2.7
0.2m 2 1.5 5 2.7
0.2m 2 1.5 1 1.5 5 2.7 1 1.5
0.2m 5 4.2
0.2m 4 0.2 5 4.2 4 0.2
m 5 21
36. 0.8(4p 1 5) 5 4(0.5p 2 2)
0.8  4p 1 0.8  5 5 4  0.5p 2 4  2
3.2p 1 4 5 2p 2 8
3.2p 1 4 22p 5 2p 2 8 2 2p
1.2p 1 4 5 28
1.2p 1 4 2 4 5 28 2 4
1.2p 5 212
1.2p 4 1.2 5 212 4 1.2
p 5 210
Lesson 4.3
1.Let x represent the amount of money, in
dollars, Amy had initially.
Because Amy had $139 after Sam gave her
$27,
x 1 27 5 139
x 1 27 2 27 5 139 2 27
x 5 112
Amy had $112 initially.
2. Let the two facing page numbers be
x and (x 1 1).
Because the sum of the two facing page
numbers is 145,
x 1 (x 1 1) 5 145
x 1 x 1 1 5 145
2x 1 1 5 145
2x 1 1 2 1 5 145 2 1
2x 5 144
2x 4 2 5 144 4 2
x 5 72
If x 5 72, x 1 1 5 72 1 1
5 73
The two page numbers are 72 and 73.
© Marshall Cavendish International (Singapore) Private Limited.
4
1
m51
5
5
4
1 
5   (m 1) m 5 5  1
5
5 
4
1
5  (m 2 1) 2 5  m 5 5
5
5
30. (m 2 1) 2
114 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 114
02/07/12 9:05 PM
3. Let Jackson’s age now be x years old.
2
Because 7 years ago, Jackson’s age was of
5
the age he will be in 20 years from now,
2
(x 1 20)
5
2
5(x 2 7) 5 5  ( x 20) 
5

x275
5(x 2 7) 5 2(x 1 20)
5  x 2 5  7 5 2  x 1 2  20
5x 2 35 5 2x 1 40
5x 2 35 2 2x 5 2x 1 40 2 2x
3x 2 35 5 40
3x 2 35 1 35 5 40 1 35
3x 5 75
3x 4 3 5 75 4 3
x 5 25
Jackson is 25 years old now.
4. Let the length of each of the other two sides
of the isosceles triangle be l inches.
Because the base is 9.5 inches and the
perimeter of the isosceles triangle is
32.7 inches,
l 1 l 1 9.5 5 32.7
2l 1 9.5 5 32.7
2l 1 9.5 2 9.5 5 32.7 2 9.5
2l 5 23.2
2l 4 2 5 23.2 4 2
l 5 11.6 in.
The length of each of the other two sides is
11.6 inches.
5.Let r represent the number of raisin muffins.
© Marshall Cavendish International (Singapore) Private Limited.
1
r.
2
3
The number of strawberry muffins is r .
2
The number of chocolate muffins is
If she only had enough ingredients to bake
480 muffins,
1
3
r 1 r 1 r 5 480
2
2
3r 5 480
3r 4 3 5 480 4 3
r 5 160
She baked 160 raisin muffins.
6. Let the number of miles Mr. Sidney drove be
d miles.
Because he paid a total of $52.54,
19.99 1 0.21d 5 52.54
19.99 1 0.21d 2 19.99 5 52.54 2 19.99
0.21d 5 32.55
0.21d 4 0.21 5 32.55 4 0.21
d 5 155
Mr. Sidney drove the car for 155 miles.
7. Let the number of product labels collected in
the third month be n.
Then the number of product labels collected
in the first two months is 3n each.
Because the total number of product labels
collected in three months is 2,100,
3n 1 3n 1 n 5 2,100
7n 5 2,100
7n 4 7 5 2,100 4 7
n 5 300
300 product labels were collected in the third
month.
8. Because the perimeter of the triangle is
33 inches,
2x 1 2(x 1 3) 1 3(x 1 2) 5 33
2x 1 2  x 1 2  3 1 3  x 1 3  2 5 33
2x 1 2x 1 6 1 3x 1 6 5 33
7x 1 12 5 33
7x 1 12 2 12 5 33 2 12
7x 5 21
7x 4 7 5 21 4 7
x53
If x 5 3, 2x 5 2  3
56
The length of AB is 6 inches.
If x 5 3, 2(x 1 3) 5 2(3 1 3)
526
5 12
The length of BC is 12 inches.
If x 5 3, 3(x 1 2) 5 3(3 1 2)
535
5 15
The length of AC is 15 inches.
9. Let the airfare be m dollars.
Then the expenses on food, gifts, and
accommodation was (3m 2 80) dollars.
Because the total expenses for the trip
was $2,660,
m 1 (3m 2 80) 5 2,660
m 1 3m 2 80 5 2,660
4m 2 80 5 2,660
4m 2 80 1 80 5 2,660 1 80
4m 5 2,740
4m 4 4 5 2,740 4 4
m 5 685
Her airfare was $685.
Extra Practice Course 2A 115
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 115
02/07/12 9:05 PM
10.Distance 5 Speed  Time
So, Time 5 Distance 4 Speed
Because the total time taken for the journey
3p 4 3 ≤ 22 4 3
5
3
2
p ≤x 23
6
4
is 7 3 hours,
4
31
d
d
240    5 240 
4
 16
15 
240 
d
d
1 240  5 1,860
15
16
15d 1 16d 5 1,860
31d 5 1,860
31d 4 31 5 1,860 4 31
d 5 60 km
Total distance traveled 5 d 1 d
5 2d km
If d 5 60, d 5 2  60
5 120 km
The total distance traveled by him is
120 kilometers.
Lesson 4.4
1.
27 1 y  10
27 1 y 2 27  10 2 27
y  217
18 17 16
2.
4x 1 5 ≥ 29
4x 1 5 2 5 ≥ 29 2 5
4x ≥ 24
4x 4 4 ≥ 24 4 4
x≥6
5
3.
6y
6y 1 1
6y
6
11
21
6y
46
y
7
7
721
6
646
1
0
1
2
4.
3p 1 1 ≤ 21
3p 1 1 2 1 ≤ 21 2 1
3p ≤ 22
1
2
1
3
3
5.
9 ≥ 12 2 x
9 1 x ≥ 12 2 x 1 x
9 1 x ≥ 12
9 1 x 2 9 ≥ 12 2 9
x≥3
2
3
4
6.
3 2 5x  13
3 2 5x 2 3  13 2 3
25x  10
25x 4 (25)  10 4 (25)
x  22
3
2
1
55
11 11
xx 
<<
66
22 33
55
11 11 11 11
xx

<< 66
22 22 33 22
55
22 33
xx<
< 66
66 66
55
55
xx<
<
66
66
55
66 55 66
x x << 66
55 66 55
7.
x1
0
1
2
7 1
33
x ≥
8 4
44
7
1
7
3 7
x ≥ 8
4
8
4 8
1
1
6
6
77
x ≥≥ 44
88 88
1 1x 2
1≥ 1
x ≥
4 4 8 8
1
1
x  (24) ≤  (24)
8
4
x ≤≤ 1
2
8.
0
1
2
© Marshall Cavendish International (Singapore) Private Limited.
d
d
3
7
16
15
4
d
d
31
16
15
4
1
116 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 116
02/07/12 9:05 PM
Name: Date: Lesson 4.4 Solving Algebraic Inequalities
Solve each inequality using the four operations. Then graph each
solution set on a number line.
1. 27 1 y  10
2.4x 1 5
29
3. 6y 1 1  7
4.3p 1 1
21
5. 9
6.3 2 5x  13
7
1
2 x
8
4
3
4
7.
5
1
1
x2 
6
2
3
8.
9.
4
1
y 2  3
5
5
10.3x 1 3  7 1 x
Solve each inequality using the four operations.
11. 8 2 x  10 2 2x
12.11 1 x
7 1 5x
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12 2 x
58 Chapter 4 Lesson 4.4
MIF_ExtraPractice C2_Ch04.indd 58
08/12/11 11:48 AM
Name: Date: 13. 0.3x 2 7  11 1 0.2x
14.2.8x 1 7
15. 11.3 2 0.5x  12 2 0.4x
16.
3
3
x
4
4
5
4
x 3  x 4
7
7
18.
2
5
1
x  x 1
3
6
3
17.
© Marshall Cavendish International (Singapore) Private Limited.
4.8x 1 9
1
x 12.4
2
19. 3(y 1 2)
18
20.6(2y 2 1)  3.6
21. 2(9 2 x)
16 2 x
22.2(2y 2 3) 2 4
y22
23. 1 (a − 1)  2(a − 1) 24.7(2a 2 3)
25. 2(2y 2 3)  4 1 3(y 2 2)
26.8 1 5(z 2 4)  2(z 1 7)
6
5 2 2(3a 2 1)
Extra Practice Course 2A 59
(M)MIFEP_C2A_Ch04.indd 59
20/06/12 12:11 PM
10.Distance 5 Speed  Time
So, Time 5 Distance 4 Speed
Because the total time taken for the journey
3p 4 3 ≤ 22 4 3
5
3
2
p ≤x 23
6
4
is 7 3 hours,
4
31
d
d
240    5 240 
4
 16
15 
240 
d
d
1 240  5 1,860
15
16
15d 1 16d 5 1,860
31d 5 1,860
31d 4 31 5 1,860 4 31
d 5 60 km
Total distance traveled 5 d 1 d
5 2d km
If d 5 60, d 5 2  60
5 120 km
The total distance traveled by him is
120 kilometers.
Lesson 4.4
1.
27 1 y  10
27 1 y 2 27  10 2 27
y  217
18 17 16
2.
4x 1 5 ≥ 29
4x 1 5 2 5 ≥ 29 2 5
4x ≥ 24
4x 4 4 ≥ 24 4 4
x≥6
5
3.
6y
6y 1 1
6y
6
11
21
6y
46
y
7
7
721
6
646
1
0
1
2
4.
3p 1 1 ≤ 21
3p 1 1 2 1 ≤ 21 2 1
3p ≤ 22
1
2
1
3
3
5.
9 ≥ 12 2 x
9 1 x ≥ 12 2 x 1 x
9 1 x ≥ 12
9 1 x 2 9 ≥ 12 2 9
x≥3
2
3
4
6.
3 2 5x  13
3 2 5x 2 3  13 2 3
25x  10
25x 4 (25)  10 4 (25)
x  22
3
2
1
55
11 11
xx 
<<
66
22 33
55
11 11 11 11
xx

<< 66
22 22 33 22
55
22 33
xx<
< 66
66 66
55
55
xx<
<
66
66
55
66 55 66
x x << 66
55 66 55
7.
x1
0
1
2
7 1
33
x ≥
8 4
44
7
1
7
3 7
x ≥ 8
4
8
4 8
1
1
6
6
77
x ≥≥ 44
88 88
1 1x 2
1≥ 1
x ≥
4 4 8 8
1
1
x  (24) ≤  (24)
8
4
x ≤≤ 1
2
8.
0
1
2
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d
d
3
7
16
15
4
d
d
31
16
15
4
1
116 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 116
02/07/12 9:05 PM
4
1
9.
y 3
5
5
4
1
1
1
y 3
5
5
5
5
4
1
y 3
5
5
4
16
y
5
5
4
5
16 5
y 5
4
5 4
y>4
© Marshall Cavendish International (Singapore) Private Limited.
3
10.
3x
3x 1 3
3x
2x
4
5
1371x
2371x23
3x  4 1 x
2x41x2x
2x  4
42442
x2
2
1
3
11.
8 2 x  10 2 2x
8 2 x 1 2x  10 2 2x 1 2x
8 1 x  10
8 1 x 2 8  10 2 8
x2
12.
11 1 x ≤ 7 1 5x
11 1 x 2 x ≤ 7 1 5x 2 x
11 ≤ 7 1 4x
11 2 7 ≤ 7 1 4x 2 7
4 ≤ 4x
4 4 4 ≤ 4x 4 4
1≤x
13.
0.3x 2 7  11 1 0.2x
0.3x 2 7 1 7  11 1 0.2x 1 7
0.3x  18 1 0.2x
0.3x 2 0.2x  18 1 0.2x 2 0.2x
0.1x  18
0.1x 4 0.1  18 4 0.1
x  180
14.
2.8x 1 7 ≥ 4.8x 1 9
2.8x 1 7 2 7 ≥ 4.8x 1 9 2 7
2.8x ≥ 4.8x 1 2
2.8x 2 2.8x ≥ 4.8x 1 2 2 2.8x
0 ≥ 2x 1 2
0 2 2 ≥ 2x 1 2 2 2
22 ≥ 2x
22 4 2 ≥ 2x 4 2
21 ≥ x
15.
11.3 2 0.5x  12 2 0.4x
11.3 2 0.5x 1 0.4x  12 2 0.4x 1 0.4x
11.3 2 0.1x  12
11.3 2 0.1x 2 11.3  12 2 11.3
2 0.1x  0.7
2 0.1x 4 (20.1)  0.7 4 (20.1)
x  27
1
3
3
x 1 ≥ x 1 12.4
2
4
4
3
3
1
3
3
x 1 2 ≥ x 1 12.4 2
4
4
2
4
4
2
3
1
3
x ≥ x 1 12 2
5
4
2
4
16.
1
62
33
3
x≥ x
2
2
5
44
4
3 

1
62
3

20   4 x  ≥ 20   x 2
5
4
62
3
1
15x ≥ 20  x 1 20 
2 20 
5
4
2
15x ≥ 10x 1 248 2 15
15x ≥ 10x 1 233
15x 2 10x ≥ 10x 1 233 2 10x
5x ≥ 233
5x 4 5 ≥ 233 4 5
x ≥ 46.6
4
5
x13 x14
7
7
4
4
4
5
x132 x x142 x
7
7
7
7
1
3 x14
7
1
324 x1424
7
1
21  x
7
1
21  7  x  7
7
17.
27  x
5
1
2
 x 1
6
3
3
1
5
2

6  x   6  x 1
3
6
3

5
1
2
6 x 6  6 x 61
6
3
3
18. x 5x 1 2  4x 1 6
5x 1 2 2 4x  4x 1 6 2 4x
x 1 2  6
x1222622
x4
Extra Practice Course 2A 117
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 117
02/07/12 9:06 PM
1
1
3( y 2) ≤ 18
3
3
y 1 2 ≤ 6
y 1 2 2 2 ≤ 6 2 2
y ≤ 4
20. 6(2y 2 1)  3.6
1
1
? 6(2y 2 1)  ? 3.6
6
6
2y 2 1  0.6
2y 2 1 1 1  0.6 1 1
2y  1.6
2y 4 2  1.6 4 2
y  0.8
21. 2(9 2 x) ≤ 16 2 x
2 ? 9 2 2 ? x ≤ 16 2 x
18 2 2x ≤ 16 2 x
18 2 2x 1 2x ≤ 16 2 x 1 2x
18 ≤ 16 1 x
18 2 16 ≤ 16 1 x 2 16
2 ≤ x
22. 2(2y 2 3) 2 4 ≥ y 2 2
2 ? 2y 2 2 ? 3 2 4 ≥ y 2 2
4y 2 6 2 4 ≥ y 2 2
4y 2 10 ≥ y 2 2
4y 2 10 2 y ≥ y 2 2 2 y
3y 2 10 ≥ 22
3y 2 10 1 10 ≥ 22 1 10
3y ≥ 8
3y 4 3 ≥ 8 4 3
y≥
8
3
23. 1 (a 2 1)  2(a 2 1)
6
6 ? 1 (a 2 1)  6 ? 2(a 2 1)
6
a 2 1  12(a 2 1)
a 2 1  12 ? a 2 12 ? 1
a 2 1  12a 2 12
a 2 1 2 a  12a 2 12 2 a
21  11a 2 12
21 1 12  11a 2 12 1 12
11  11a
11 4 11  11a 4 11
1a
24. 7(2a 2 3) ≤ 5 2 2(3a 2 1)
7 ? 2a 2 7 ? 3 ≤ 5 2 2 ? 3a 2 2 ? (21)
14a 2 21 ≤ 5 2 6a 1 2
14a 2 21 ≤ 7 2 6a
14a 2 21 1 6a ≤ 7 2 6a 1 6a
20a 2 21 ≤ 7
20a 2 21 1 21 ≤ 7 1 21
20a ≤ 28
20a 4 20 ≤ 28 4 20
a ≤ 1.4
25.
2(2y 2 3)  4 1 3(y 2 2)
2 ? 2y 1 2 ? (23)  4 1 3 ? y 1 3 ? (22)
4y 2 6 4 1 3y 2 6
4y 2 6 3y 2 2
4y 2 6 2 3y  3y 2 2 2 3y
y 2 6 22
y 2 6 1 6 22 1 6
y  4
26.8 1 5(z 2 4)  2(z 1 7)
8 1 5 ? z 2 5 ? 4 2 ? z 1 2 ? 7
8 1 5z 2 20 2z 1 14
212 1 5z  2z 1 14
212 1 5z 2 2z  2z 1 14 2 2z
212 1 3z  14
212 1 3z 1 12 14 1 12
3z  26
3z ? 1  26 ? 1
3
3
26
z
3
Lesson 4.5
1.Let x be the score he gets on the next quiz.
Average ≥ 80
1
? (70 1 75 1 83 1 80 1 x) ≥ 80
5
1
? (308 1 x) ≥ 80
5
1
5 ? ? (308 1 x) ≥ 5 ? 80
5
308 1 x ≥ 400
308 1 x 2 308 ≥ 400 2 308
x ≥ 92
He must get at least 92 on the next quiz.
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19. 3(y 1 2) ≤ 18
118 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 118
02/07/12 9:06 PM
Name: Date: Lesson 4.5 Real-World Problems: Algebraic Inequalities
Solve. Show your work.
1. Reuben has scores of 70, 75, 83, and 80 on four Spanish quizzes. What score
must he get on the next quiz to achieve an average of at least 80?
2. Howard is saving to buy a mountain bike that costs $245, excluding tax.
He has already saved $28. What is the least amount of money Howard must
save each week so that at the end of the 9th week, he has enough money to
buy the bike? Round your answer to the nearest dollar.
4. To raise money for a children’s charity, a company is selling hot air balloon
rides. The cost of going on a balloon ride is a flat rate of $50 plus $15 per
hour of flight time. If Mrs. Beckham plans to donate at most $85, find the
number of hours she can spend in the balloon ride. Round your answer to
the nearest hour.
5. East High School’s student council plans to buy some stools and chairs for a
new student center. They need to buy 25 more chairs than stools. The chairs
cost $32 each and the stools cost $28 each. If the budget is $2,620, how
many chairs can they buy?
© Marshall Cavendish International (Singapore) Private Limited.
3. When Jane uses her calling card overseas, the cost of a phone call is $0.75
for the first three minutes and $0.12 for each additional minute, thereafter. If
Jane plans to spend at most $3.60 to make a call, find the greatest possible
length of talk time. Round your answer to the nearest whole number.
60 Chapter 4 Lesson 4.5
(M)MIFEP_C2A_Ch04.indd 60
20/06/12 12:11 PM
1
1
3( y 2) ≤ 18
3
3
y 1 2 ≤ 6
y 1 2 2 2 ≤ 6 2 2
y ≤ 4
20. 6(2y 2 1)  3.6
1
1
? 6(2y 2 1)  ? 3.6
6
6
2y 2 1  0.6
2y 2 1 1 1  0.6 1 1
2y  1.6
2y 4 2  1.6 4 2
y  0.8
21. 2(9 2 x) ≤ 16 2 x
2 ? 9 2 2 ? x ≤ 16 2 x
18 2 2x ≤ 16 2 x
18 2 2x 1 2x ≤ 16 2 x 1 2x
18 ≤ 16 1 x
18 2 16 ≤ 16 1 x 2 16
2 ≤ x
22. 2(2y 2 3) 2 4 ≥ y 2 2
2 ? 2y 2 2 ? 3 2 4 ≥ y 2 2
4y 2 6 2 4 ≥ y 2 2
4y 2 10 ≥ y 2 2
4y 2 10 2 y ≥ y 2 2 2 y
3y 2 10 ≥ 22
3y 2 10 1 10 ≥ 22 1 10
3y ≥ 8
3y 4 3 ≥ 8 4 3
y≥
8
3
23. 1 (a 2 1)  2(a 2 1)
6
6 ? 1 (a 2 1)  6 ? 2(a 2 1)
6
a 2 1  12(a 2 1)
a 2 1  12 ? a 2 12 ? 1
a 2 1  12a 2 12
a 2 1 2 a  12a 2 12 2 a
21  11a 2 12
21 1 12  11a 2 12 1 12
11  11a
11 4 11  11a 4 11
1a
24. 7(2a 2 3) ≤ 5 2 2(3a 2 1)
7 ? 2a 2 7 ? 3 ≤ 5 2 2 ? 3a 2 2 ? (21)
14a 2 21 ≤ 5 2 6a 1 2
14a 2 21 ≤ 7 2 6a
14a 2 21 1 6a ≤ 7 2 6a 1 6a
20a 2 21 ≤ 7
20a 2 21 1 21 ≤ 7 1 21
20a ≤ 28
20a 4 20 ≤ 28 4 20
a ≤ 1.4
25.
2(2y 2 3)  4 1 3(y 2 2)
2 ? 2y 1 2 ? (23)  4 1 3 ? y 1 3 ? (22)
4y 2 6 4 1 3y 2 6
4y 2 6 3y 2 2
4y 2 6 2 3y  3y 2 2 2 3y
y 2 6 22
y 2 6 1 6 22 1 6
y  4
26.8 1 5(z 2 4)  2(z 1 7)
8 1 5 ? z 2 5 ? 4 2 ? z 1 2 ? 7
8 1 5z 2 20 2z 1 14
212 1 5z  2z 1 14
212 1 5z 2 2z  2z 1 14 2 2z
212 1 3z  14
212 1 3z 1 12 14 1 12
3z  26
3z ? 1  26 ? 1
3
3
26
z
3
Lesson 4.5
1.Let x be the score he gets on the next quiz.
Average ≥ 80
1
? (70 1 75 1 83 1 80 1 x) ≥ 80
5
1
? (308 1 x) ≥ 80
5
1
5 ? ? (308 1 x) ≥ 5 ? 80
5
308 1 x ≥ 400
308 1 x 2 308 ≥ 400 2 308
x ≥ 92
He must get at least 92 on the next quiz.
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19. 3(y 1 2) ≤ 18
118 Answers
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 118
02/07/12 9:06 PM
2. Let Howard‘s weekly savings be x dollars.
Total savings≥ 245
28 1 9x ≥ 245
28 1 9x 2 28≥ 245 2 28
9x ≥ 217
9x 4 9 ≥ 217 4 9
x ≥ 24
1
9
He must save at least $25 each week.
3. Let the length of talk time after the first
three minutes be t.
Total call charges ≤ 3.60
0.75 1 0.12t ≤ 3.60
0.75 1 0.12t 2 0.75 ≤ 3.60 2 0.75
0.12t ≤ 2.85
0.12t 4 0.12≤ 2.85 4 0.12
t ≤ 23.75
The greatest possible length of talk time
after the first three minutes is 23 minutes.
Therefore, the greatest possible length of
talk time is 26 minutes.
4.Let h be the number of hours.
Because she plans to donate at most $85,
50 1 15h ≤ 85
50 1 15h 2 50 ≤ 85 2 50
15h ≤ 35
15h 4 15≤ 35 4 15
1
h ≤ 2
3
© Marshall Cavendish International (Singapore) Private Limited.
She can spend at most 2 hours in the
balloon ride.
5. Let the number of chairs be m.
The number of stools is (m 2 25).
Total cost ≤ 2,620
32m 1 28(m 2 25)≤ 2,620
32m 1 28 ? m 2 28 ? 25 ≤ 2,620
32m 1 28m 2 700≤ 2,620
60m 2 700≤ 2,620
60m 2 700 1 700≤ 2,620 1 700
60m ≤ 3,320
60m 4 60≤ 3,320 4 60
1. Let an integer be x.
1
3
They can buy at most 55 chairs.
3
4
x 1 15.
The other integer is
Because the sum of the integers is greater
than 49,

3
x 1  x 15   49
4

3
x 1 15  49
4
7
3
47 x 1 x 1 15  49
4
4
x 1
7
4
x 1 15  49
7
4
x 1 15 2 15  49 2 15
7
4
x  34
7
4
4
7
x ?  34 ? 4
7
136
7
3
x  19
7
x 
The smallest integer x can be is 20.
If x 5 20,
m ≤ 55
Brain@Work
3
4
x 1 15 5
3
4
? 20 1 15
5 30
The least values for these two integers are
20 and 30.
2. Let the number of hours be d.
For Plan A to be a better option,
Rental for Plan A  Rental for Plan B
210 1 10d  120 1 25d
210 1 10d 2 10d  120 1 25d 2 10d
210
 120 1 15d
210 2 120 120 1 15d 2 120
90
 15d
90 4 15  15d 4 15
6
d
Josie would have to rent the photo booth for
more than 6 hours for Plan A to be a better
option.
3. Let the number of adults be x.
The number of children is 3x.
Box office receipts ≤ 3,190
8.50x 1 5.50 ? (3x) ≤ 3,190
8.50x 1 16.50x ≤ 3,190
25x ≤ 3,190
25x 4 25 ≤ 3,190 4 25
x ≤ 127.6
The greatest number of adult tickets sold
was 127.
Extra Practice Course 2A 119
(M)MIFEP_C2A_Ch01-Ch05_Ans.indd 119
02/07/12 9:06 PM
Name:
Date:
CHAPTER
5
Direct and Inverse Proportion
Solve. Show your work.
Distance (x miles)
Distance (y kilometers)
20
30
50
32.2
48.3
80.5
a)
Find the constant of proportionality. What does this value represent
in this situation?
b)
Write the direct proportion equation.
c)
How many kilometers are there in 70 miles?
2. An average person can text 40 characters in 30 seconds. Given that the
number of characters is directly proportional to the amount of time taken to
text, how long would it take an average person to text 30 characters?
20
© Marshall Cavendish International (Singapore) Private Limited.
1. The table shows the relationship between distance in kilometers and
distance in miles. The distance in kilometers is directly proportional to the
distance in miles.
Chapter 5 Direct and Inverse Proportion
(M)MIFEn_C2_C05.indd 20
6/15/12 10:47 AM
Name:
Date:
3. A television network claims that for every 100 minutes of television
programming, there are 26 minutes of commercials. If this same rate holds
true for all television programs, how many minutes of commercials would
you expect for a one hour television program?
4. Some U.S. nickel coins contain 3 ounces of copper per ounce of nickel. How
many pounds of nickel coins do you need to obtain 15 pounds of copper?
© Marshall Cavendish International (Singapore) Private Limited.
5. An astronaut who weighs 162 pounds on Earth weighs 27 pounds on the
moon. If an astronaut weighs 114 pounds on Earth, how much would the
astronaut weigh on the moon?
6. Peter has just returned from the Philippines and wants to exchange his
remaining Philippine pesos for U.S. dollars. If the exchange rate that day
is 43.35 pesos per U.S. dollar, how many U.S. dollars would he get for his
remaining 1,500 Philippine pesos? Round your answer to the nearest dollar.
Enrichment Course 2
(M)MIFEn_C2_C05.indd 21
21
6/15/12 10:47 AM
Name:
Date:
7. To sew a garment, a seamstress uses 5.7 centimeters of thread for every
7.6 centimeters of fabric.
a)
If the seamstress uses 4.2 centimeters of thread, how much fabric is
involved?
b)
If the seamstress is working with 21.2 centimeters of fabric, how many
centimeters of thread is needed?
9. The time it takes for a car to travel a particular distance is inversely
proportional to the speed of a car. If a car is traveling at a speed of 50 miles
per hour, it takes 1.25 seconds to pass between two hash marks on the road.
22
a)
If it takes a car 1.5 seconds to pass between the two hash marks, what
is the speed of the car? Round your answer to the nearest tenth.
b)
How long does it take for a car traveling at 65 miles per hour to pass
between the two hash marks? Round your answer to the nearest second.
© Marshall Cavendish International (Singapore) Private Limited.
8. A computer salesperson earns a 20% commission from his sales. A laptop
is priced at $1,944. The salesperson gives a 5% discount off the price of the
laptop to a buyer. How much commission does the salesperson earn after
the discount?
Chapter 5 Direct and Inverse Proportion
(M)MIFEn_C2_C05.indd 22
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Name:
Date:
10. It takes 5 painters 6 days to paint a hallway in a school. The number of days
needed to paint a hallway, d, is inversely proportional to the number of
painters painting the school hallway, n.
a)
Find the constant of proportionality.
b)
Write an inverse proportion equation relating d and n.
c)
How many days would it take for 3 painters to complete the same work?
d)
How many painters would it take to paint the same hallway in 2 days?
© Marshall Cavendish International (Singapore) Private Limited.
11. A school district budgets $750 per year for student academic achievement
awards. The amount spent per award, c, is inversely proportional to the
number of awards to be given, n.
a)
Write an inverse proportion equation relating c and n.
b)
What is the greatest possible cost of each award if the school district
intends to give out 80 awards in one year?
c)
What is the greatest possible number of awards to be given in one year
if each award costs $12.50?
Enrichment Course 2
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6/15/12 10:47 AM
Name:
Date:
12.
24
a)
Write a direct proportion equation relating m and n.
b)
If Josh only has enough money to buy 3.7 gallons of gas, how far can he
travel before refueling?
c)
Last year, Josh drove his car a total of 11,500 miles. How many
gallons of gas did he use last year? Round your answer to the nearest
whole number.
© Marshall Cavendish International (Singapore) Private Limited.
Josh’s car can travel 364 miles on one tank of gas. His car’s fuel tank holds
14 gallons of gas. The number of miles traveled, m, is directly proportional
to the number of gallons of gas used, n.
Chapter 5 Direct and Inverse Proportion
(M)MIFEn_C2_C05.indd 24
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Name:
Date:
13.
© Marshall Cavendish International (Singapore) Private Limited.
The number of rectangular tiles, N, required to cover a playroom floor is
inversely proportional to the area, A , of each tile in square feet. The entire
playroom floor can be covered using 120 tiles, each measuring 24 inches by
12 inches.
a)
Find the constant of proportionality.
b)
Write an inverse proportion equation relating N and A.
c)
How many 12-inch by 12-inch tiles are needed to cover the same
playroom floor?
d)
If the value of A is doubled, what happens to the value of N?
Enrichment Course 2
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6/15/12 10:47 AM
0.2 y
8
33.8
0.2
0.2
y 169
There are 169 nickels in the piggy bank.
16. Brain@Work
4(x 2) 2 2x
4x 8 2 2x
4x 8 2x 2 2x 2x
2x 8 2
2x 8 8 2 8
2x 6
6
2 x
2
2
x3
9 2(y 3) 3(y 2) 1
9 2y 6 3y 6 1
9y1
9yy1y
91y
911y1
8y
z
3
1
2
z
3
1
2
1
2
z
3
z
3
z
3
3
z
5
2
5
2
4
2
2
2 3
6
1
2
Given that the sum of the numbers on each
side of the figure is 15, the figure will look
like this:
3
5
4
7
2
8
1
6
Chapter 5
y kx
1. a)
y
k x
32.2
20
1.61
The value represents the number of
kilometers in 1 mile.
b) y 1.61x
c) When x 70, y 1.61 70
y 112.7
There are 112.7 kilometers in 70 miles.
2. Let y be the amount of time taken to text
30 characters.
30
40
y
30
40y 30 30
40y 900
40y
900
40
40
y 22.5
It takes an average person 22.5 seconds to text
30 characters.
3. Let y be the number of minutes of
commercials.
1 h 60 min
26
100
y
60
100y 60 26
100y 1,560
100 y
100
© Marshall Cavendish International (Singapore) Private Limited.
Total number of campers
x 2x
3x
3 35
105
There are 105 campers at the summer camp.
15. Brain@Work
Let y represent the number of nickels in the
piggy bank.
So, there are (250 y ) quarters in the piggy
bank.
0.05 y 0.25(250 y ) 28.7
0.05 y 62.5 0.25 y 28.7
0.2 y 62.5 62.5 28.7 62.5
0.2 y 33.8
1,560
100
y 15.6
66
Answers
(M)MIFEn_C2_ANS.indd 66
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There will be an expected 15.6 minutes of
commercials for a one hour program.
4. 1 oz 0.0625 lb
3 oz 0.0625 3 0.1875 lb
Let x be the amount of nickel coins needed
in pounds.
0.0625
0.1875
0.1875
15
7.6
0.9375
0.1875
27
5
100
162
162
x 19
The astronaut will weigh 19 pounds on the
moon.
6. Let x be the amount of money he receives, in
U.S. dollars.
1
43.35
x
1, 500
100x
© Marshall Cavendish International (Singapore) Private Limited.
43.35
7.6
5.7
b)
x
5.7
31.92
5.7
x 5.6
There is 5.6 centimeters of fabric involved.
36,936
100
10. a)
62.5
1.5
x 41.7
The speed of the car is 41.7 miles per
hour.
When x 65, 65 y 62.5
65y 62.5
65 y
62.5
65
4.2
5.7x 4.2 7.6
5.7x 31.92
5.7x
100
1.5
43.35
20
1.5x
1,500
x 35
Peter would get 35 U.S. dollars.
7. a) Let x be the amount of fabric involved.
x 369.36
The commission earned is $369.36.
9. a) Let x represent the speed of the car.
Let y represent time taken.
x y 50 1.25
xy 62.5
When y 1.5, x 1.5 62.5
1.5x 62.5
43.35x 1,500 1
43.35x 1,500
43.35 x
7.6
100x 1,846.80 20
100x 36,936
100
3,078
120.84
$1,944 $97.20
x
114
$1,944 $97.20 $1,846.80
Let x represent the commission earned.
162x 114 27
162x 3,078
162 x
y
21.2
y 15.9
15.9 centimeters of thread is needed.
8. To find the price of the laptop during the sale:
1,846.80
x
7.6y 21.2 5.7
7.6y 120.84
7.6 y
x5
The amount of nickel coins needed is
5 pounds.
5. Let x be the astronaut’s weight on the moon.
162
5.7
7.6
x
0.1875x 15 0.0625
0.1875x 0.9375
0.1875 x
Let y be the amount of thread she
needs.
b)
65
y1
It will take the car 1 second to pass
between the two hash marks.
Constant of proportionality:
d n 5 6 30
b)
The equation is dn 30 or d c)
When n 3,
30
30
n
30
d
10
n 3 It would take 3 painters 10 days to
complete the same work.
Enrichment Course 2
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.
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6/15/12 10:40 AM
When d 2,
c)
30
2
n
2n 30
2n
2
30
2
n 15
15 painters would be needed.
11. a)
b)
750
The equation is cn 750 or c n .
When n 80,
c
c)
750
d)
9.375
80
240
240
If A 20, N 20 12
12.50 750
n
12.5n 750
12.5
Chapter 6
750
1. mAOC mCOB 180
12.5
n 60
The greatest possible number of awards
is 60.
12. Brain@Work
a) Constant of proportionality:
m
n
b)
c)
364
14
26
The equation is m 26n.
When n 3.7,
m 26 3.7 96.2
Josh can travel 96.2 miles before
refueling.
When m 11,500,
11,500 26n
26n
26
11, 500
26
n 442
Josh used 442 gallons of gas last year.
13. Brain@Work
12 in. 1 ft
24 in. 2 ft
a) Area of one tile (24 in. by 12 in.):
2 1 2 ft2
Constant of proportionality:
N A 120 2 240
b)
68
The equation is NA 240 or N 240 tiles, measuring 12 inches by
12 inches, would be needed.
The value of N will be halved.
To check:
If A 10, N 10 24
The greatest cost is $9.37 per award.
When c 12.50,
12.5n
The constant of proportionality
represents the area of the playroom
floor. The area of the playroom floor
is 240 square feet.
Area of one tile (12 in. by 12 in.):
1 1 1 ft2
When A 1, N 1 240
N 240
240
A
.
[Adj. s on
a st. line]
3y 2y 180
5y 180
5y
180
5
5
y 36
mEOD mDOB 90 [Comp. s]
z y 90
z 36 36 90 36
z 54
2. mAOM mBAO [Alt. int. s]
30
mCOM mDCO [Alt. int. s]
26
30 26 p 360 [s at a point]
56 p 360
56 p 56 360 56
p 304
3. mGHJ mEFK [Corr. s]
40
mGJF mJGH mGHJ [Ext. of
triangle]
2x x 40
2x x x 40 x
x 40
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d)
Answers
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