Download Exercise Answers - Oregon Focus on Math

Oregon Focus on Introductory Algebra
Lesson 1 Answers
Exercise Answers
1. 17
14. 6
2. 4
15. 7.6
3. 13
16. a. Subtracted 6 from 25 before
multiplying by 2; 14
b. Multiplied 2 and 3 before
dividing 12 by 2; 25
4. 45
5. 16
6. 7
7. 71
8. 0
17. 6 + 3 × 5 = 21
18. 28 ÷ 7 − 1 = 3 19. 10 + 4 − 5 × 2 = 4 or
10 ∙ 4 ÷ 5 ÷ 2 = 4
9. 145
20. $66
10. 14.3
21. $10
11. 13
22. $45
12. 16
23. a. Answers may vary.
b. Answers may vary.
c. Answers may vary.
d. Answers may vary.
13. 50
1
Oregon Focus on Introductory Algebra
Lesson 2 Answers
Exercise Answers
1. a. 2
b. 3
c. 8
2. 3
5
3. 14
13. 10 × 10 = 100
25. See below.
14. 12 × 12 = 14
26. 24
15. 13 × 13 × 13 = 271
27. 3
16. 71 = 7
28. 26
17. No. 5 cubed is 125 while 3 to
29. 125
the 5 power is 243.
th
4. 72
18. 2
5. 27
19. 2
6. 83
20.
7. 113
21. 4 , 3 , 2
2
31. 8
5
8. 6 × 6 = 36
32. 137
( 12 )2
2
3
33. 1
5
22. 512 calories
9. 1 × 1 × 1 × 1 × 1 × 1 × 1 = 1
23. a. 4 × 4 × 4
b. 43
c. 64 cubic units
10. 2 × 2 × 2 = 8
11. 5 × 5 × 5 = 125
30. 10
34. 7.75
35. 27 ÷ 9 − 3 = 0
36. 8 × 6 + 2 = 50
24. a. 16,384
b. 6,561
c. 1,024
12. 3 × 3 × 3 × 3 = 81
25. a.
Months Chores
Have Been
Completed
1
2
3
4
5
Pay for
Completing
Chores
$4
$16
$64
$256
$1,024
b. Answers may vary.
2
Expanded Form
Power
4×4
4×4×4
4×4×4×4
4×4×4×4×4
42
43
44
45
Oregon Focus on Introductory Algebra
Lesson 3 Answers
Exercise Answers
15. 69
16. 3 × 52 + 7 = 82
1. 35
17. 10 − 4 ÷ 22 = 9
2. 5
18. 4² × 3 × 2 + 1 = 97
3. 24
19. a. Ants
4. 60
b. 409
5. 4
20. a. Line 1; 13
b. Line 2; 251
6. 31
21. 25
7. 112.5
22. 93
8. 90
23. 126
9. 39
24. 32
10. 67
25. 53
11. 19
26. 35
12. 16
27. 33, 62, 26
13. 250
28. 170, 43, 92
14. 0
3
Oregon Focus on Introductory Algebra
Lesson 4 Answers
15. 39
Exercise Answers
16. 104
1. a. Find the value of expressions
17. 15
inside grouping symbols.
b. Find the value of all powers.
c. Multiply and divide from left
to right.
d. Add and subtract from left to
right.
18. 50
19. 2 × (4 + 6) = 20
20. 4 + (2 + 8) ÷ 2 = 9
2. Parentheses and fraction bars
21. (15 + 1) × 4 + 5 × 2 = 74
3. It is important so that all people
22. a. $120
will get the same answer.
b. You could multiply 8 by
3, 8 by 4, then 8 by 8 and
add them all together.
You could also add the
hours all together and
then multiply by 8.
4. 5
5. 28
6. 13
7. 27
23. _______
​ 14 +33  + 4 
 
​= 7
8. 11
24. 7 × 7 = 49
9. 4
25. 3 × 3 × 3 = 27
10. 1,200
26. 12 × 12 = 144
11. 35
27. 2 × 2 × 2 × 2 = 16
12. 20
28. 10 × 10 × 10 = 1,000
13. 39
29. 1 × 1 × 1 × 1 × 1 = 1
14. 0
4
Oregon Focus on Introductory Algebra
Lesson 5 Answers
Exercise Answers
14. (8 + 2) + 5
15. a. 15 and 35; They are
1. Answers may vary.
compatible numbers.
b. 15 + 35 + 27
c. 77
2. Answers may vary.
3. Answers may vary.
16. a. 102 square feet
b. Answers may vary.
4. Answers may vary.
17. 24
5. Associative
18. 3
6. Commutative
19. 76
7. Commutative
20. 5
8. Associative
21. 18
9. Not Equal
22. 6
10. True; Associative
23. 0
11. True; Commutative
24. 46
12. Not Equal
25. 46
13. Answers may vary.
5
Oregon Focus on Introductory Algebra
Block 1 Review Answers
Exercise Answers
1. 31
2. 4
3. 43
4. 18
5. 8
6. $53
7. 43
8. 76
9. 32
10. 27
17. 26
33. a. 3 × (5 + 8) = 39
b. (5 + 3) × 4 + 12 ÷ 4 = 35
18. ( 12 )2
19. a. 5 × 5 × 5
b. 53
c. 125 cubic units
20. 108
21. 15
34. a. $117
b. You could multiply 9 by 2,
9 by 4, then 9 by 7 and
add them all together.
You could also add the
hours all together and
then multiply by 9.
35. Commutative
22. 11
36. Associative
23. 100
37. Associative
24. 426
38. Commutative
25. 65
26. a. 2 × 6 + 82 = 76
b. 9 + 102 ÷ 2 = 59
39. True; Associative
40. True; Commutative
11. 95
27. 3
41. Not Equal
12. 153
28. 45
42. Answers may vary.
13. 4 × 4 × 4 = 64
29. 94
43. (13 + 6) + 3
14. 1 × 1 × 1 × 1 = 1
30. 20
15. 11 × 11 = 121
31. 10
16. 33
32. 13
6
Oregon Focus on Introductory Algebra
Lesson 6 Answers
Exercise Answers
1.
Keith’s
Allowance
$14
$20
$25
$31
x
Calculation
14 − 3
20 − 3
25 − 3
31 − 3
x−3
18. two times a number w plus 1
19. x plus 5; five more than x; the
Michael’s
Allowance
$11
$17
$22
$28
x−3
sum of 5 and x
20. ten subtract p; p less than 10;
p subtracted from ten
2. 6 × x; the times symbol “×”
21. a. 114 beats
3. y + 11
22. a. 6 slips
b. 380 beats
c. 38b beats
looks too much like the
variable x
b. 13 slips
c. 2t slips
4. 9m
23. a. $2.00 per pound
5. 7z
c
3
b. x + 1.25
c. y − 1.25
7. x + 5
24. 11 × 11 = 121
8. p − 4
25. 1 × 1 × 1 × 1 × 1 × 1 = 1
9. w − 31
26. 4 × 4 × 4 = 64
6.
10.
27. 20 × 20 = 400
14
b
11. n − 13
28. 2 × 2 × 2 × 2 = 16
12. 5x
29. 0 × 0 × 0 × 0 × 0 = 0
13. y minus 2
30. Equal; Commutative Property
14. three times d
31. Not Equal
15. sixty minus x
32. Equal; Associative Property
16. p plus 16
17. r divided by 5
7
Oregon Focus on Introductory Algebra
Lesson 7 Answers
Exercise Answers
17. 92
1. 11
18. 60
2. 48
19.
3. 19
4. 20
5. 18 12
x
6x + 3
0
3
1
2
6
3
21
8
51
20
123
6. 4
20.
7. 22
x
5x − 3
2
8. 6
1
1
5
11
9. 15
6
13 12
9
21
10. a. $58
b. $112
c. $352
21. a. x = number of containers of
ice cream; y = number of
packages of cones
b. $20
11. a. 420 breaths
b. 1,260 breaths
c. 21m breaths
22. 2 ∙ (6 + 3) = 18
12. a. 9 + 4r
b.
Number of
Rides, r
Cost
9 + 4r
2
$17
5
$29
11
$53
23. 4 ∙ (5 + 20) ÷ 10 = 10
24. 1 + 30 ÷ 5 ∙ (2 − 1) = 7
13. 34
25. 18
14. 24
26. 105
15. 7
27. 24
16. 9
8
Oregon Focus on Introductory Algebra
Lesson 8 Answers
Exercise Answers
10. 60 cubic in
11. 216 cubic units
1. a. area = 15 square units;
perimeter = 16 units
b. area = 1 square unit;
perimeter = 5 units
c. area = 240 square units;
perimeter = 68 units
12. 12 square units
13. 82 square cm
14. a. 40 cubic inches
b. 76 square inches
c. 80
2. 160 square feet
3. 21 square meters
15. a. 251.2 meters
b. ≈ 6 times
4. 78.5 square cm
16. 21
5. 28 units
17. 28
6. 250 square ft
18. 3
7. 33 square units
19. 39
8. 92 units
20. 45
9. 62.8 inches
21. 45
9
Oregon Focus on Introductory Algebra
Lesson 9 Answers
Exercise Answers
13. 0.284
14. second half
1. $24
15. 0.290
2. $280
16. 19
3. $378
17. 4
4. a. $300
b. $48
18. 26
5. 4 years
19. 30
6. $1,080
20. 8
7. d = 40 miles
21. 1
8. 165 miles
22. 78.5 square m
9. 13.5 miles
23. 54 square units
10. 2.5 miles
24. 28 cm
11. a. 558 miles; 536.25 miles
25. 70 square units
b. ≈ 2,188.5 miles
26. 56.52 units
12. 0.372
10
Oregon Focus on Introductory Algebra
Lesson 10 Answers
Exercise Answers
14. 0
15. b + 4c
1. 9y
16. a. 3x + 2y
2. 4x
b. 5x + 3y + 2x − 3y
c. 7x; one term
3. 5m
17. Answers may vary.
4. 8x + 7y
18. Answers may vary.
5. 9
19. 5
6. 2d + 7
20.
7. 8u + 8t
8
9
21. 6
8. 2x + 3y
22. 36
9. 11n
23. 25
10. 20m + 4n
24. 5
11. 3f + 19
25. 3
12. 7x
26. 40
13. 6g + 6k + 10h
27.
11
5
6
Oregon Focus on Introductory Algebra
Lesson 11 Answers
Exercise Answers
19. 5(1,000 + 3) = 5,015
20. 2(13 − 0.02) = 25.96
1. 5; 4
21. 8 (300 + 5) = 2,440
2. 8; 8
22. a. 6(15) − 6(0.05)
3. 6; 5(2)
4. 11;
b. $89.70
1
2
23. 72 feet
5. a. Answers may vary.
24. a. $4.75
b. 6(4 + 7) = $66
b. $9.27
c. $4.20
d. $18.22; Yes
6. 5(6) + 5(8) = 70
7. 3(20) + 3(4) = 72
25. $73.50
8. 6(30) − 6(1) = 174
26. 88
9. 7(6) − 7(0.2) = 40.6
27. 189
10. 9(3) + 9(1.2) = 37.8
28. 17
11. 2(60) + 2(8) = 136
29. 53
12. 12(3) + 12(0.1) = 37.2
30. 23
13. 5(6) + 5(0.3) = 31.5
31. 32
14. 11(9) − 11(4) = 55
32. $48
15. Answers may vary.
33. $1,200
16. 4(200 + 1) = 804
34. $28
17. 7(100 −1) = 693
35. a. Answers may vary.
b. J.R. - $48; Lindsey - $45
18. 3(9 + 0.2) = 27.6
12
Oregon Focus on Introductory Algebra
Lesson 12 Answers
Exercise Answers
21. x + 3 + x + 3 + x + 3 + x + 3 + x + 3 =
5x + 15 or 5(x + 3) = 5x + 15
1. 5x + 35
22. 8 + 6x + 9 + 8 + 4x − 2 = 10x + 23
2. 3y − 12
23. 4x + 1 + x + 2 + 4x + 1 + x + 2 =
10x + 6 or 2(4x + 1) + 2(x + 2) =
10x + 6
3. 6m + 6
4. 7x − 0.7
24. 5(x + 4) = 5x + 20
5. 12p + 8
25. 11(4x − 7) = 44x − 77
6. 10x − 12
26. i. 2x + 14
ii. 2x + 8
iii. 2x + 8
ii. and iii. are equivalent
7. 60 − 3x
8. 10y + 50
9. 22m − 44
27. i. 6x + 3
ii. 6x + 6
iii. 6x + 3
i. and iii. are equivalent
10. First distribute the 3 to the
x and the 6, then combine like
terms.
28. 7x + 26
11. Answers may vary.
29. 7x + 20
12. 10x + 12
30. Yes
13. 6x + 3
31. x + 12
14. 2x − 30
32. 6x
15. 5x − 20
33. 7x
16. 13x + 9
34.
17. 6x + 12
35. 31 - 37
or x ÷ 5
32 - 150
33 - 175
34 - 5
18. 6x + 7
19. 14x + 11
20. 4x + 5x + 3x = 12x
x
5
36. a. 3.6 miles
13
b. 9.6 miles
c. 1.2x miles
Oregon Focus on Introductory Algebra
Block 2 Review Answers
Exercise Answers
19.
x
1
2
x−1
2
0
1. d + 9
6
2
9
3_2​ 1 ​ 
2. p − 1
14
6
3. w − 40
20. a. the x stands for each
package of hot dogs; the y
stands for each package of
buns
b. $60
4. 22
m or 22 ÷ m
5. y − 10
6. 3x
21. 20 square in
7. six times a number y
22. 12.56 square m
8. nine less than d
23. 38 units
9. twelve divided by x
24. 42 square ft
10. three more than m
25. 25.12 units
11. a. $2.00
26. 60 cubic units
b. y − 0.75
12. 23
27. 46 square cm
13. 22
28. $200
14. 17
29. $6
15. 2
30. $2,880
16. 11
31. 40 miles
17. 1
32. 248 miles
18.
x
5x + 2
0
2
1
7
4
22
7
37
33. 0.318
34. 0.480
35. 15x
14
Oregon Focus on Introductory Algebra
Block 2 Review Answers
36. 9y + 3
49. a. 8(2) − 8(0.03) = $15.76
b. $15.76
37. 10m
50. 7x − 21
38. 5x + y
51. 4x + 40
39. 9y
52. 12x + 30
40. 2x
53. 10x + 6
41. 3(20) + 3(2) = 66
54. 22x + 13
42. 7(8) + 7(3) = 77
55. 6x + 17
43. 4(5) − 4(0.1) = 19.6
56. 9x − 20
44. 10(9) + 10(0.3) = 93
57. i. 5x + 14
45. 5(200) + 5(1) = 1005
ii. 5x + 15
iii. 5x + 15
ii. and iii. are equivalent
46. 8(100) − 8(2) = 784
47. 4(2000) + 4(5) = 8,020
58. i. 4x + 20
ii. 4x + 30
iii. 4x + 20
i. and iii. are equivalent
48. 7(10) + 7(0.9) = 76.3
15
Oregon Focus on Introductory Algebra
Lesson 13 Answers
Exercise Answers
15. x + 6 = 10; E
1. No
16. x − 14 = 3; B
2. Yes
17. 3x = 27; C
3. Yes
18. x5 = 4 ; A
4. No
19. x + 11 = 14; D
5. Yes
20. x − 2 = 8; F
6. No
21. a. 175 = 7 m
b. No
c. More. 7(20) = 140 is less than
175 calories.
7. No
8. Yes
9.
10. 11. 12. 22. 3x + 15
x
9−x=3
Solution?
3
9−3≠3
NO
6
9−6=3
YES
9
9−9≠3
NO
24. 7x + 8
25. 20x + 35
x
x +11 = 24
Solution?
11
11 + 11 ≠ 24
NO
12
11 + 12 ≠ 24
NO
13
11 + 13 = 24
YES
x
4x = 4.8
23. 6x − 16
26. 5x + 4
27. 26x − 5
Solution?
1
4(1) ≠ 4.8
NO
1.2
4(1.2) = 4.8
YES
1.8
4(1.8) ≠ 4.8
NO
x
x
=7
6
Solution?
42
42 ÷ 6 = 7
YES
48
48 ÷ 6 ≠ 7
NO
60
60 ÷ 6 ≠ 7
NO
28. 7x + 11
29. 11x + 2
30. 24
31. 48
32. 0
13. a. #2
b. 20%
c. Answers may vary.
33. 10
34. 44
14. a. 4 bases times a number
should equal 360
b. Yes. 4(90) = 360
35. 12
16
Oregon Focus on Introductory Algebra
Lesson 14 Answers
Exercise Answers
1. x = 6
2. y = 11
3. h = 13
4. x = 19
5. m = 2
6. p = 2
7. y = 23
8. w = 21
9. b = 0
10. z = 14
19. 329 − x = 94; x = 235 feet
20. x ≈ 7
21. y ≈ 9
22. m ≈ 2
23. x ≈ 13
24. m ≈ 2
25. p ≈ 7
26. y ≈ 15
27. k = 0
28. d ≈ 6
29. a. s ≈ 54
b. The answer represents the total
amount spent on souvenirs.
11. c = 9
12. x = 48
13. a. c + 98 = 112
b. c = 14 pounds
14. a. 12p = 18
b. p =$1.50
30. a. 4.15d = 55.95
b. d ≈ 14 days
31. 52 + x = 83;
x = 31 tow trucks
32.
15. x + 6 = 15; x = 9
16. 4x = 16; x = 4
17. x2 = 7 ; x = 14
33.
18. x − 10 = 2; x = 12
17
x
x + 21 = 30
Solution?
6
6 + 21
≠ 30
NO
8
8 + 21
≠ 30
NO
9
9 + 21 =
30
YES
x
9x = 45
Solution?
4
9(4) ≠ 45
NO
5
9(5) = 45
YES
6
9(6) ≠ 45
NO
Oregon Focus on Introductory Algebra
Lesson 15 Answers
Exercise Answers
16. x + 17 = 20; x = 3
17. 8 + x = 31; x = 23
1. x = 7
18. x + 12 = 5 , x = 4 12
2. y = 12
19. a. The variable represents
3. p = 8
the amount Jared paid
for his rent.
b. $585
4. h = 4.2
5. k = 64
6. x =
20. 2.25 + x = 2.6;
x = 0.35 pounds
1
3
21. 14 + x = 95; x = 81 miles
7. y = 106
22. Answers may vary.
8. d = 0
23. 19
9. f = 1.2
24. 75
10. m = 18
25. 15
11. p = 2 12
26. 17
12. x = 53
27. 9
13. a. x = 42
b. x = 0
c. Correct
d. Correct
28. 14
29. 0.15 miles
14. x + 19 = 34; x = 15
30. 3.5 miles
15. x + 12 = 26; x = 14
18
Oregon Focus on Introductory Algebra
Lesson 16 Answers
Exercise Answers
14. a. c − 33 = 12 or c − 12 = 33
b. c = 45 candy bars
1. y = 21
15. a. t − 9 = 16
2. x = 20
b. t = 25 turkeys
c. 5 turkeys per hour
3. t = 38
16. x − 6 = 21; x = 27
4. m = 11.4
17. x − 10 = 72; x = 82
5. k = 40
6. p =
18. x − 5 = 19; x = 24
3
4
19. x − 34 = 12 , x = 1 14
7. d = 578
20. a. x − 1240 = 930 or
8. x = 5.45
x − 930 = 1240
b. x = 2,170 miles
9. f = 71
21. Answers may vary.
10. b = 2.9
22. a. Subtraction; x = 47
11. f = 6
b. Addition; y = 21
c. Addition; p = 64
d. Subtraction; m = 6.7
12. y = 100
13. a. She spent (−) $32 and had
23. 132 square feet
$15 left.
b. y = $47
c. How much money Carrie
had to begin with.
24. 12.56 feet
25. 12.56 square feet
26. 64 feet
19
Oregon Focus on Introductory Algebra
Lesson 17 Answers
Exercise Answers
15. x = 8
16. 6y = 66; y = 11
1. Multiplication
17. x4 = 8 ; x = 32
2. Division
18. 7x
3. Division
= 5 ; x = 35
19. 9x = 36; x = 4
4. y = 2
20. a. 3j = 42
5. p = 12
b. James is 14 years old.
6. m = 21
21. 5x = 15; Hannah’s sister is 3.
7. h = 80
22. a.
p
3
=4
b. There were 12 pieces in all.
8. x = 6
23. x5 = 45217 ; x = 226,085
9. p = 7
24. D
10. j = 2
25. B
11. b = 44
26. A
12. y = 3
27. C
13. m = 4
14. c = 160
20
Oregon Focus on Introductory Algebra
Lesson 18 Answers
Exercise Answers
21. x = 8
22. h = 707
1. Division
23. y = 14
2. Addition
24. p = 1
3. Subtraction
25. y + 8 = 20; y = 12
4. Multiplication
26.
5. Subtraction
x
6
= 11 ; x = 66
27. 15x = 45; x = 3
6. Division
28. p − 14 = 3; p = 17
7. x = 31
29. x2
8. y = 8
= 50 ; x = 100
30. 20 + x = 44; x = 24
9. p = 7.9
31. a. 3.2h = 24.32
10. f = 2
b. Horatio’s hourly wage is $7.60.
11. k = 27
32. a. y − 4,030 = 570
b. 4,600 people will be at the circus.
12. y = 2 14
33. a. p − 16 = 19
13. m = 101
b. 35 points
14. c = 95
34. 3x = 870; The average square foot per
person was 290.
15. x = 90
35. 11x
16. w = 5
36. 4y + 4
17. y = 11.24
37. 6y
18. d = 2
38. B = 0.240
19. a = 0
39. B = 0.220
20. b = 18
21
Oregon Focus on Introductory Algebra
Lesson 19 Answers
11. The height of the sail was 32 feet.
Exercise Answers
1. The length of the rectangle is 5 units.
12. y = 343
2. Ryan has had 10 hits this season.
13. x = 11
3. The width of the cereal box is
14. k = 5
3 inches.
15. m = 36
4. Jakin was driving at a rate of 35 mph.
16. p = 27
5. The length of the base of the triangle is
8 centimeters.
17. c = 104
6. Maria had the money in her account
18. y = 49
for 4 years.
7. Emma was walking at a rate of
miles per hour.
8. The width of Toby’s yard is
19. d = 1 83
2 12
20. x = 40
5 12 meters.
21. w = 5
9. Lisa was getting a rate of 4%.
22. y = 0.65
10. The height of the prism is 6 units.
23. d = 12
22
Oregon Focus on Introductory Algebra
Lesson 20 Answers
Exercise Answers
16. 2x + 7 = 25; x = 9
1. x = 4
17. 2y + 4 = 10 ; y = 12
2. h = 12
18. 12 + 5w = 72; w = 12
3. x = 50
19. 12 p − 3 = 4 ; p = 14
4. m = 5
20. 2x − 3 = 7; x = 5 meatballs
5. y = 2
21. 2x + 15 = 27; x = 6 children
6. w = 44
22. 18x + 6 = 150; x = 8 jars
7. p = 24
23.
8. p = 2
9. x = 1
10. a = 40
24.
11. w = 0
12. x = 4
13. x = 11
14. y = 8
25.
15. a. Did not do the inverse
operation; x = 11
b. Subtracted 15 from the
wrong side of the equation;
x = 1 12
c. Did not do the inverse
operation; x = 192
23
x
4x − 1
1
2
1
3
11
5
19
12
47
x
2
5x + 2
2
6
3
8 12
6
16
100
251
x
(x + 1)²
1
4
2
9
5
36
9
100
Oregon Focus on Introductory Algebra
Block 3 Review Answers
Exercise Answers
19. y = 24
1. No
20. m = 1
2. Yes
21. a = 0.6
3. Yes
22. k = 19
4. No
5.
6.
18. x = 7
x
7
8
9
3x = 27
3(7) ≠ 27
3(8) ≠ 27
3(9) = 27
x
11
12
21
x + 12 = 23
11 + 12 = 23
12 + 12 ≠ 23
21 + 12 ≠ 23
Solution?
NO
NO
YES
Solution?
YES
NO
NO
23. x = 2​ _14 ​
24. x + 9 = 13; x = 4
25. x + 22 = 40; x = 18
26. a. The unknown amount is what
Michelle makes, so Michelle’s
earnings (x) plus $310 equals what
Kelsey makes ($1,250).
b. Michelle makes $940 per month.
7. x + 8 = 10
8. x − 11 = 7
9. 4x = 24
10. x2 = 6
11. x = 3
12. y = 15
13. x = 7
14. m = 6
15. y = 20
16. w = 30
27. x = 17
28. y = 28
29. p = 46
30. m = 363
31. p =
32. k = 7.3
33. x − 5 = 31; x = 36
34. x − 17 = 40; x = 57
35. a. w − 42 = 24;
b. w = 66; Christopher needs to drink
66 ounces of water per day.
17. a. 8m = 24
b. m = 3; each milkshake costs $3
1
2
36. y = 3
24
Oregon Focus on Introductory Algebra
Block 3 Review Answers
37. p = 9
57. a = 186
38. m = 20
58. w = 11
39. x = 70
59.
40. b = 4
60. x = 140
41. a = 7.5
61. The width of the rectangle is 5 units.
42. 4y = 36; y = 9
62. Frank has 12 hits this season.
43. 7x
63. The width of the box is 3 centimeters.
= 3 ; x = 21
44. a. 3x = 24
y = 4 79
64. Aiden was running at 6 miles per hour.
b. x = 8; Julie is 8 years old.
65. The length of the base of the triangle is
45. 5w = 15; w = 3; Wesley ate 3 pieces of
14 cm.
candy.
66. Vanessa left her money in the account
46. subtraction
for 4 years.
47. addition
67. x = 4
48. division
68. y = 14
49. multiplication
69. a = 60
50. subtraction
70. m = 8
51. division
71. x = 36
52. x = 5
72. w = 20
53. y = 46
73. 3x + 4 = 25; x = 7
54. m = 36
74. 7p − 4 = 2 ; p = 42
55. p = 2
75. 2w + 8 = 10; w = 1
56. k = 4.6
76. 2x + 7 = 21; x = 7 hours
25
Oregon Focus on Introductory Algebra
Lesson 21 Answers
Exercise Answers
11. (1, 2)
12. (9, 9)
y-axis
1. - 2.
13. - 21.
D
S
A
T
Z
B
E
C
M
x-axis
U
Origin
H
3. (5, 3)
W
L
4. (7, 0)
5. (8, 7)
22.
6. (2, 5)
7. (0, 0)
8. Triangle
23.
9. Square
x
2 + 7x
0
2
1
9
2
16
3
23
5
37
x
1
2 x−1
2
0
6
2
7
2 12
10
4
24. x = 6
25. m = 1,091
26. u = 99
27. p = 0.7
10. Rectangle
28. z = 18 121
29. a = 4
26
P
Oregon Focus on Introductory Algebra
Lesson 22 Answers
Exercise Answers
7. Answers may vary. (0, 8),
1.
8. a.
Input
x
Function Rule
y = 4x
Output
y
0
1
2
3
4(0)
4(1)
4(2)
4(3)
0
4
8
12
2.
Input
x
1
2
3
4
Function Rule
y = 3x − 1
3(1) − 1
3(2) − 1
3(3) − 1
3(4) − 1
Output
y
2
5
8
11
3.
Input
x
Function Rule
y = 12 x
Output
y
4.
5.
6.
1
1
2
(1)
2
1
2
(2)
1
3
1
2
(3)
1
4
1
2
(4)
2
(3, 5), (5, 3), (8, 0)
0
Function
Rule
y = 0.5x + 4
0.5(0) + 4
4
0.5(4) + 4
6
7
10
0.5(7) + 4
0.5(10) + 4
7.5
9
Input
Weeks, x
Output
Height, y
4
b. (0, 4), (4, 6), (7, 7.5), (10, 9)
c. - d.
1
2
Input
x
2
5
8
10
Function Rule
y=x+2
2+2
5+2
8+2
10 + 2
Output
y
4
7
10
12
Input
x
Function Rule
x
y=
5
Output
y
0
0
5
0
5
5
5
1
20
20
5
4
Input
x
0
3
5
8
Function Rule
y=8−x
8−0
8−3
8−5
8−8
9. a.
1
2
Input
Hours, x
Function Rule
y = 15x
Output
Miles, y
1
2
5
6
15(1)
15(2)
15(5)
15(6)
15
30
75
90
b. (1, 15), (2, 30), (5, 75),
(6, 90)
c.- d.
e. 180 miles
Output
y
8
5
3
0
27
Oregon Focus on Introductory Algebra
Lesson 22 Answers
10. a. y = 5x
b.
Input
Weeks,
x
Function
Rule
y = 5x
Output
Savings,
y
0
5(0)
0
1
2
3
4
5(1)
5(2)
5(3)
5(4)
5
10
15
20
Savings
c. (0, 0), (1, 5), (2, 10), (3, 15), (4, 20)
d.
11. x = 16
Weeks
12. x = 15
13. x = 10
14. x = 3
15. x = 3
16. x = 0.9
17.
7
x = 12
18. x = 787
19. x = 3.5
28
Oregon Focus on Introductory Algebra
Lesson 23 Answers
Exercise Answers
10. Create an input-output table
11. #1: y = 4x
1. y = 5 + 4x
#2: y = 3 + x
2. y = 11 − 2x
12. a.
3. y = 2 + 0.5x
4. a. +5; it is the coefficient of x
b. 3
c. Increasing; there is a plus sign
in front of the 5x
Output
Money Remaining, y
350
330
310
290
4
270
5
250
b. y = 350 −20x
c. $190
5. y = 1 + 2x
13. a. $15
6. y = 4 − 0.5x
b. $10
c. y = 15 + 10x
d. $105
7. y = 16 − 4x
8. y = 0 + 1x or y = x
14. 16
9. a.
15. 5
Input
Weeks, x
0
1
2
3
4
5
Input
Weeks, x
0
1
2
3
Output
Total Fires Fought, y
12
15
18
21
24
27
16. 43
17. 32
18. 75
b. y = 12 + 3x
c. 45 fires
19. 1
29
Oregon Focus on Introductory Algebra
Lesson 24 Answers
1.
2.
3.
4.
5.
6.
Input
x
0
1
2
3
Function Rule
y = 1 + 3x
1 + 3(0)
1 + 3(1)
1 + 3(2)
1 + 3(3)
Output
y
1
4
7
10
Ordered Pair
(x, y)
(0, 1)
(1 ,4)
(2, 7)
(3, 10)
Input
x
0
1
2
3
Function Rule
y = 8 − 2x
8 − 2(0)
8 − 2(1)
8 − 2(2)
8 − 2(3)
Output
y
8
6
4
2
Ordered Pair
(x, y)
(0, 8)
(1, 6)
(2, 4)
(3, 2)
Input
x
0
1
2
3
Input
x
0
1
2
3
Function Rule
y = 1.5x
1.5(0)
1.5(1)
1.5(2)
1.5(3)
Function Rule
y=3+x
3+0
3+1
3+2
3+3
Input
x
Function Rule
0
Output
y
0
1.5
3
4.5
Output
y
3
4
5
6
Ordered Pair
(x, y)
(0, 0)
(1, 1.5)
(2, 3)
(3, 4.5)
Ordered Pair
(x, y)
(0, 3)
(1, 4)
(2, 5)
(3, 6)
y = 7 − 12 x
Output
y
Ordered Pair
(x, y)
7− 2 (0)
1
7
(0, 7)
1
1
7− 2 (1)
6 12
(1, 6 12 )
2
1
7− 2 (2)
6
(2, 6)
3
1
7− 2 (3)
5 12
(3, 5 12 )
Output
y
15
11
7
3
Ordered Pair
(x, y)
(0, 15)
(1, 11)
(2, 7)
(3, 3)
Input
x
0
1
2
3
Function Rule
y = 15 − 4x
15 − 4(0)
15 − 4(1)
15 − 4(2)
15 − 4(3)
7. Start Value = 5, Amount of Change = +2
30
Oregon Focus on Introductory Algebra
Lesson 24 Answers
8. Start Value = 9, Amount of
Change = −4
13.
9. Start Value = 5, Amount of
Change = −1
14. a. 8 Weight (pounds)
b. +0.5; increasing
c. y = 8 + 0.5x
d.
10. Start Value = 0, Amount of
Change = +3
e. Answers may vary.
Height (inches)
15. y = 9 + 3x
11. Start Value = 4, Amount of
Change = + 12
16. y = 8 − x
17. y = 2 + 3x
12. Start Value = 8, Amount of
Change = −3
18. y = 1.5x
31
Oregon Focus on Introductory Algebra
Lesson 25 Answers
Exercise Answers
9. a. 3 circles; 6 circles; 9 circles
b. 12 circles; 15 circles
1. 11, 13, 15; First Term = 3;
Operation = +2
2. 12, 7, 2; First Term = 27;
c. + 3 circles
d.
Operation = −5
3. 175, 200, 225, 250;
First Term = 125;
Operation = +25
e. y = 3 + 3x
f. 93 circles
4. 26, 29, 32, 35, 38;
First term = 23; Operation = +3
10. Answers may vary.
5. 9.0, 8.6, 8.2, 7.8, 7.4, 7.0;
First Term = 9.0;
Operation = −0.4
11. a. y = 6 + 7x
b. 706 triangles
6. 4, 5 12 , 7, 8 12 , 10, 11 12
12.
First Term = 4;
Operation = +1 12
7. a. 3 units
b. 4 units; 5 units
c. 6 units; 7 units
13.
d. + 1 unit
e. 11 units
8. a. 5 squares; 9 squares; 13
squares
b. 17 squares
c. + 4 squares
d.
Number of Squares
14.
e. y = 5 + 4x
f. 65 squares
32
Oregon Focus on Introductory Algebra
Lesson 25 Answers
15.
16.
17.
18. a. $50
b. $10
c.
33
Oregon Focus on Introductory Algebra
Block 4 Review Answers
Exercise Answers
1.
10.
y-axis
T
U
V
Input
x
2
4
5
8
Function Rule
y = 3x − 2
3(2) − 2
3(4) − 2
3(5) − 2
3(8) − 2
Output
y
4
10
13
22
11. (2, 4), (4, 10), (5, 13), (8, 22)
R
S
12. a.
x-axis
Origin
2. (5, 3)
3. (9, 5)
Input
Hours,
x
1
2
3
4
Function
Rule
y = 4x
Output
Miles, y
4(1)
4(2)
4(3)
4(4)
4
8
12
16
b. (1, 4), (2, 8), (3, 12), (4, 16)
c.- d.
4. (0, 6)
Miles
5. (4, 0)
6. (2, 7)
7. Square
e. 32 miles
13. y = 14 − 3x
14. y = 5 + 0.5x
15. a. Amount of Change = −2;
8. Triangle
9.
Input
x
0
1
2
3
it is the coefficient of the
variable.
b. Start Value = 13
c. Decreasing; there is a minus
before the variable.
Function
Rule
y = 7x
7(0)
7(1)
7(2)
7(3)
16. y = 2 + 4x
Output
y
17. y = 9 − x
0
7
14
21
34
Oregon Focus on Introductory Algebra
Block 4 Review Answers
Input
Weeks, x
0
1
2
3
4
5
25. y = 7x
Output
Money In Account, y
50
65
80
95
110
125
Miles
18. a.
b. y = 50 + 15x
c. $185
19. 20. 21. 26. 13, 9, 5; First Term = 25;
Operation = −4
Input
x
0
1
2
3
Function Rule
y = 4 + 2x
Input
x
0
1
2
3
Function Rule
y=7−x
Input
x
0
1
2
3
Function Rule
y = 2.5x
4 + 2(0)
4 + 2(1)
4 + 2(2)
4 + 2(3)
7−0
7−1
7−2
7−3
2.5(0)
2.5(1)
2.5(2)
2.5(3)
Output
y
4
6
8
10
Ordered Pair
(x, y)
(0, 4)
(1, 6)
(2, 8)
(3, 10)
Output
y
7
6
5
4
Ordered Pair
(x, y)
(0, 7)
(1, 6)
(2, 5)
(3, 4)
Output
y
0
2.5
5
7.5
Ordered Pair
(x, y)
(0, 0)
(1, 2.5)
(2, 5)
(3, 7.5)
22. Start Value = 1;
Amount of Change = +3
23. Start Value = 8;
Amount of Change = −3;
24. Start Value = 2;
Amount of Change = +1;
35
27. 31, 39, 47; First Term = 7;
Operation = +8
28. 55, 85, 100;
First Term = 40;
Operation = +15
29. 18, 12, 10;
First Term = 20;
Operation = −2
30. a. 6
b. 10; 14
c. 18
d. + 4
e. 34