4. VOCABULARY
1. Model: A physical or numerical representation of a real world
situation
2. Mathematical Model:
3. Algebraic Model:
4. Rule:
5. VOCABULARY
1. Model: A physical or numerical representation of a real world
situation
2. Mathematical Model: Using numbers in a table or list to
describe a situation
3. Algebraic Model:
4. Rule:
6. VOCABULARY
1. Model: A physical or numerical representation of a real world
situation
2. Mathematical Model: Using numbers in a table or list to
describe a situation
3. Algebraic Model: A model that includes one or more variables,
often written as an expression
4. Rule:
7. VOCABULARY
1. Model: A physical or numerical representation of a real world
situation
2. Mathematical Model: Using numbers in a table or list to
describe a situation
3. Algebraic Model: A model that includes one or more variables,
often written as an expression
4. Rule: Another name for a formula or equation
10. THE FIVE-STEP PLAN
1. Read: Read through the problem, then go back through it piece
by piece
11. THE FIVE-STEP PLAN
1. Read: Read through the problem, then go back through it piece
by piece
2. Plan:
12. THE FIVE-STEP PLAN
1. Read: Read through the problem, then go back through it piece
by piece
2. Plan: Using the parts of the problem, figure out what needs to
be done
13. THE FIVE-STEP PLAN
1. Read: Read through the problem, then go back through it piece
by piece
2. Plan: Using the parts of the problem, figure out what needs to
be done
3. Solve:
14. THE FIVE-STEP PLAN
1. Read: Read through the problem, then go back through it piece
by piece
2. Plan: Using the parts of the problem, figure out what needs to
be done
3. Solve: Set up and solve the problem
15. THE FIVE-STEP PLAN
1. Read: Read through the problem, then go back through it piece
by piece
2. Plan: Using the parts of the problem, figure out what needs to
be done
3. Solve: Set up and solve the problem
4. Answer:
16. THE FIVE-STEP PLAN
1. Read: Read through the problem, then go back through it piece
by piece
2. Plan: Using the parts of the problem, figure out what needs to
be done
3. Solve: Set up and solve the problem
4. Answer: Make sure you have answered each question that is
being asked
17. THE FIVE-STEP PLAN
1. Read: Read through the problem, then go back through it piece
by piece
2. Plan: Using the parts of the problem, figure out what needs to
be done
3. Solve: Set up and solve the problem
4. Answer: Make sure you have answered each question that is
being asked
5. Check:
18. THE FIVE-STEP PLAN
1. Read: Read through the problem, then go back through it piece
by piece
2. Plan: Using the parts of the problem, figure out what needs to
be done
3. Solve: Set up and solve the problem
4. Answer: Make sure you have answered each question that is
being asked
5. Check: Make sure your answers work and make sense
19. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
b. Write an algebraic model of the fare system.
20. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
21. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
22. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
23. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
24. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
25. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
26. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
27. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
28. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
29. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
30. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
31. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
32. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
33. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
34. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
35. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
36. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
37. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
38. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
39. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
40. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
Let q equal quarter miles traveled
41. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
a. Make a table that expresses the fare for trips of that range
from 1 to 3 miles, including every quarter-mile.
# of
1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Miles
Fare $6.45 $7.25 $8.05 $8.85 $9.65 $10.45 $11.25 $12.05 $12.85
b. Write an algebraic model of the fare system.
Let q equal quarter miles traveled 3.25 + .8q
42. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
c. Write a rule for the fare system.
43. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
c. Write a rule for the fare system.
Let f be the fare and q be a quarter-mile
44. EXAMPLE 1
A taxi charges $3.25 plus $.80 for each quarter-mile.
c. Write a rule for the fare system.
Let f be the fare and q be a quarter-mile
F = 3.25 + .8q
45. EXAMPLE 2
Compare vacation packages offered at two beach resorts. The
Matt Mitarnowski Surf Resort offers a family package of $750
for five days with a charge of $75 for each additional day.
Fuzzy Jeff’s Sun and Sand Resort offers a similar plan for
$350 for three days with a charge of $100 each additional day.
Which resort offers a better deal for a stay of four days? What
about nine days? How about fourteen days?
46. EXAMPLE 2
Compare vacation packages offered at two beach resorts. The
Matt Mitarnowski Surf Resort offers a family package of $750
for five days with a charge of $75 for each additional day.
Fuzzy Jeff’s Sun and Sand Resort offers a similar plan for
$350 for three days with a charge of $100 each additional day.
Which resort offers a better deal for a stay of four days? What
about nine days? How about fourteen days?
Follow The Five-Step Plan
50. EXAMPLE 2
1. Read the problem.
2. Plan.
Let c be the cost and d the number of days
51. EXAMPLE 2
1. Read the problem.
2. Plan.
Let c be the cost and d the number of days
Be aware that there is a charge for days after a certain amount
52. EXAMPLE 2
1. Read the problem.
2. Plan.
Let c be the cost and d the number of days
Be aware that there is a charge for days after a certain amount
3. Set up and solve.
53. EXAMPLE 2
1. Read the problem.
2. Plan.
Let c be the cost and d the number of days
Be aware that there is a charge for days after a certain amount
3. Set up and solve.
MMSR
54. EXAMPLE 2
1. Read the problem.
2. Plan.
Let c be the cost and d the number of days
Be aware that there is a charge for days after a certain amount
3. Set up and solve.
MMSR
c = 750 +
55. EXAMPLE 2
1. Read the problem.
2. Plan.
Let c be the cost and d the number of days
Be aware that there is a charge for days after a certain amount
3. Set up and solve.
MMSR
c = 750 + 75(d − 5)
56. EXAMPLE 2
1. Read the problem.
2. Plan.
Let c be the cost and d the number of days
Be aware that there is a charge for days after a certain amount
3. Set up and solve.
MMSR FJSSR
c = 750 + 75(d − 5)
57. EXAMPLE 2
1. Read the problem.
2. Plan.
Let c be the cost and d the number of days
Be aware that there is a charge for days after a certain amount
3. Set up and solve.
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
58. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
4 days:
59. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
4 days:
Charges $750 for a five-day stay
60. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
4 days:
Charges $750 for a five-day stay c = 350 + 100(4 − 3)
61. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
4 days:
Charges $750 for a five-day stay c = 350 + 100(4 − 3)
c = 350 + 100(1)
62. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
4 days:
Charges $750 for a five-day stay c = 350 + 100(4 − 3)
c = 350 + 100(1)
c = 350 + 100
63. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
4 days:
Charges $750 for a five-day stay c = 350 + 100(4 − 3)
c = 350 + 100(1)
c = 350 + 100
c = 450
64. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
4 days:
Charges $750 for a five-day stay c = 350 + 100(4 − 3)
c = 350 + 100(1)
c = 350 + 100
c = 450
Charges $450 for a five-day stay
65. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
66. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
c = 750 + 75(9 − 5)
67. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
c = 750 + 75(9 − 5)
c = 750 + 75(4)
68. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
c = 750 + 75(9 − 5)
c = 750 + 75(4)
c = 750 + 300
69. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
c = 750 + 75(9 − 5)
c = 750 + 75(4)
c = 750 + 300
c = 1050
70. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
c = 750 + 75(9 − 5)
c = 750 + 75(4)
c = 750 + 300
c = 1050
Charges $1050 for a nine-
day stay
71. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
c = 750 + 75(9 − 5) c = 350 + 100(9 − 3)
c = 750 + 75(4)
c = 750 + 300
c = 1050
Charges $1050 for a nine-
day stay
72. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
c = 750 + 75(9 − 5) c = 350 + 100(9 − 3)
c = 750 + 75(4) c = 350 + 100(6)
c = 750 + 300
c = 1050
Charges $1050 for a nine-
day stay
73. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
c = 750 + 75(9 − 5) c = 350 + 100(9 − 3)
c = 750 + 75(4) c = 350 + 100(6)
c = 750 + 300 c = 350 + 600
c = 1050
Charges $1050 for a nine-
day stay
74. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
c = 750 + 75(9 − 5) c = 350 + 100(9 − 3)
c = 750 + 75(4) c = 350 + 100(6)
c = 750 + 300 c = 350 + 600
c = 1050 c = 950
Charges $1050 for a nine-
day stay
75. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
9 days:
c = 750 + 75(9 − 5) c = 350 + 100(9 − 3)
c = 750 + 75(4) c = 350 + 100(6)
c = 750 + 300 c = 350 + 600
c = 1050 c = 950
Charges $1050 for a nine- Charges $950 for a nine-day stay
day stay
76. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
77. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
c = 750 + 75(14 − 5)
78. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
c = 750 + 75(14 − 5)
c = 750 + 75(9)
79. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
c = 750 + 75(14 − 5)
c = 750 + 75(9)
c = 750 + 675
80. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
c = 750 + 75(14 − 5)
c = 750 + 75(9)
c = 750 + 675
c = 1425
81. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
c = 750 + 75(14 − 5)
c = 750 + 75(9)
c = 750 + 675
c = 1425
Charges $1425 for a
fourteen-day stay
82. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
c = 750 + 75(14 − 5) c = 350 + 100(14 − 3)
c = 750 + 75(9)
c = 750 + 675
c = 1425
Charges $1425 for a
fourteen-day stay
83. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
c = 750 + 75(14 − 5) c = 350 + 100(14 − 3)
c = 750 + 75(9) c = 350 + 100(11)
c = 750 + 675
c = 1425
Charges $1425 for a
fourteen-day stay
84. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
c = 750 + 75(14 − 5) c = 350 + 100(14 − 3)
c = 750 + 75(9) c = 350 + 100(11)
c = 750 + 675 c = 350 + 1100
c = 1425
Charges $1425 for a
fourteen-day stay
85. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
c = 750 + 75(14 − 5) c = 350 + 100(14 − 3)
c = 750 + 75(9) c = 350 + 100(11)
c = 750 + 675 c = 350 + 1100
c = 1425 c = 1450
Charges $1425 for a
fourteen-day stay
86. EXAMPLE 2
MMSR FJSSR
c = 750 + 75(d − 5) c = 350 + 100(d − 3)
14 days:
c = 750 + 75(14 − 5) c = 350 + 100(14 − 3)
c = 750 + 75(9) c = 350 + 100(11)
c = 750 + 675 c = 350 + 1100
c = 1425 c = 1450
Charges $1425 for a Charges $1450 for a
fourteen-day stay fourteen-day stay
88. EXAMPLE 2
4. Answer the questions.
For a four-day or nine-day stay, Fuzzy Jeff’s Sun and Sand
Resorts offers a better deal, but for a fourteen-day stay, Matt
Mitarnowski’s Surf Resort is better.
89. EXAMPLE 2
4. Answer the questions.
For a four-day or nine-day stay, Fuzzy Jeff’s Sun and Sand
Resorts offers a better deal, but for a fourteen-day stay, Matt
Mitarnowski’s Surf Resort is better.
5. Check to make sure the answers make sense.
