ALG 140 | September 13, 2025
Charlotte Diaz
Dr. Deborah Thompson
ALG 140
Algebra Fundamentals Review
With Solutions
Problem 1: A cell phone plan costs 76.53 per month plus 2.12 per text message. If the total
cost is $214.29, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
214.29 = 76.53 + 2.12x
Solving for x:
214.29 - 76.53 = 2.12x
137.76 = 2.12x
x = 137.76 ÷ 2.12
x = 65.0 text messages
Reasoning:
Check: 76.53 + 2.12(65.0) = 76.53 + 137.80 = 214.33 ✓
Problem 2: A cell phone plan costs 29.49 per month plus 3.75 per text message. If the total
cost is $285.37, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
285.37 = 29.49 + 3.75x
Solving for x:
285.37 - 29.49 = 3.75x
255.88 = 3.75x
x = 255.88 ÷ 3.75
x = 68.2 text messages
Alternative solution:
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:42:15 GMT -05:00
https://www.coursehero.com/file/251540483/MTH-167-Algebra-Winter2024-Solutions-5856docx/
, ALG 140 | September 13, 2025
Check: 29.49 + 3.75(68.2) = 29.49 + 255.75 = 285.24 ✓
Problem 3: A plumber charges 54.18 for a service call plus 4.23 per hour of work. If the total
cost is $305.67, find the number of hours used.
Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
305.67 = 54.18 + 4.23x
Solving for x:
305.67 - 54.18 = 4.23x
251.49 = 4.23x
x = 251.49 ÷ 4.23
x = 59.5 hours
Alternative approach:
Check: 54.18 + 4.23(59.5) = 54.18 + 251.69 = 305.87 ✓
(Professor emphasized this method in class)
Problem 4: Analyze and sketch the cubic polynomial f(x) = 1x³ + 0x² - 2x + 4 Find: a) End
behavior, b) y-intercept, c) Critical points (approximate)
Solution:
Given: f(x) = 1x³ + 0x² - 2x + 4
a) End behavior:
Leading coefficient is 1 (positive)
As x → ∞: f(x) → +∞
As x → -∞: f(x) → -∞
b) y-intercept: f(0) = 4
Point: (0, 4)
c) Critical points found by solving f'(x) = 0:
f'(x) = 3x² + 0x - 2
Using quadratic formula on f'(x) = 0...
(Critical points require numerical methods for exact values)
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:42:15 GMT -05:00
https://www.coursehero.com/file/251540483/MTH-167-Algebra-Winter2024-Solutions-5856docx/
Charlotte Diaz
Dr. Deborah Thompson
ALG 140
Algebra Fundamentals Review
With Solutions
Problem 1: A cell phone plan costs 76.53 per month plus 2.12 per text message. If the total
cost is $214.29, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
214.29 = 76.53 + 2.12x
Solving for x:
214.29 - 76.53 = 2.12x
137.76 = 2.12x
x = 137.76 ÷ 2.12
x = 65.0 text messages
Reasoning:
Check: 76.53 + 2.12(65.0) = 76.53 + 137.80 = 214.33 ✓
Problem 2: A cell phone plan costs 29.49 per month plus 3.75 per text message. If the total
cost is $285.37, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
285.37 = 29.49 + 3.75x
Solving for x:
285.37 - 29.49 = 3.75x
255.88 = 3.75x
x = 255.88 ÷ 3.75
x = 68.2 text messages
Alternative solution:
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:42:15 GMT -05:00
https://www.coursehero.com/file/251540483/MTH-167-Algebra-Winter2024-Solutions-5856docx/
, ALG 140 | September 13, 2025
Check: 29.49 + 3.75(68.2) = 29.49 + 255.75 = 285.24 ✓
Problem 3: A plumber charges 54.18 for a service call plus 4.23 per hour of work. If the total
cost is $305.67, find the number of hours used.
Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
305.67 = 54.18 + 4.23x
Solving for x:
305.67 - 54.18 = 4.23x
251.49 = 4.23x
x = 251.49 ÷ 4.23
x = 59.5 hours
Alternative approach:
Check: 54.18 + 4.23(59.5) = 54.18 + 251.69 = 305.87 ✓
(Professor emphasized this method in class)
Problem 4: Analyze and sketch the cubic polynomial f(x) = 1x³ + 0x² - 2x + 4 Find: a) End
behavior, b) y-intercept, c) Critical points (approximate)
Solution:
Given: f(x) = 1x³ + 0x² - 2x + 4
a) End behavior:
Leading coefficient is 1 (positive)
As x → ∞: f(x) → +∞
As x → -∞: f(x) → -∞
b) y-intercept: f(0) = 4
Point: (0, 4)
c) Critical points found by solving f'(x) = 0:
f'(x) = 3x² + 0x - 2
Using quadratic formula on f'(x) = 0...
(Critical points require numerical methods for exact values)
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:42:15 GMT -05:00
https://www.coursehero.com/file/251540483/MTH-167-Algebra-Winter2024-Solutions-5856docx/
