MATH 118F | September 13, 2025
Mia H. Thompson
Kevin Wright
MATH 118F
Algebra Problem Set
With Solutions
Problem 1: A rental car costs 71.44 per day plus 1.66 per mile. If the total cost is $159.23,
find the number of miles used.
Solution:
Let x = number of miles
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
159.23 = 71.44 + 1.66x
Solving for x:
159.23 - 71.44 = 1.66x
87.79 = 1.66x
x = 87.79 ÷ 1.66
x = 52.9 miles
Mathematical justification:
Check: 71.44 + 1.66(52.9) = 71.44 + 87.81 = 159.25 ✓
Problem 2: A ball is thrown upward from a height of 73 feet with initial velocity 76 ft/s.
Equation: h(t) = -7t² + 76t + 73 When does the ball hit the ground?
Solution:
When the ball hits the ground, h(t) = 0
Setting up the equation:
-7t² + 76t + 73 = 0
Using the quadratic formula: t = (-b ± √(b² - 4ac)) / (2a)
Where a = -7, b = 76, c = 73
t = (-76 ± √(76² - 4(-7)(73))) / (2(-7))
t = (-76 ± √(5776 + 2044)) / -14
t = (-76 ± √7820) / -14
t = (-76 ± 88.43) / -14
Taking the positive solution:
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, MATH 118F | September 13, 2025
t = (-76 + 88.43) / -14
t = -0.89 seconds
The ball hits the ground after -0.89 seconds.
Problem 3: A plumber charges 82.74 for a service call plus 1.03 per hour of work. If the total
cost is $318.66, find the number of hours used.
Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
318.66 = 82.74 + 1.03x
Solving for x:
318.66 - 82.74 = 1.03x
235.92 = 1.03x
x = 235.92 ÷ 1.03
x = 229.0 hours
Double-checking the work:
Check: 82.74 + 1.03(229.0) = 82.74 + 235.87 = 318.61 ✓
Problem 4: A rental car costs 41.90 per day plus 0.93 per mile. If the total cost is $159.87,
find the number of miles used.
Solution:
Let x = number of miles
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
159.87 = 41.90 + 0.93x
Solving for x:
159.87 - 41.90 = 0.93x
117.97 = 0.93x
x = 117.97 ÷ 0.93
x = 126.8 miles
Verify:
Check: 41.90 + 0.93(126.8) = 41.90 + 117.92 = 159.82 ✓
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:45:11 GMT -05:00
https://www.coursehero.com/file/251540570/MTH-230-Algebra-Solutions-1358docx/
Mia H. Thompson
Kevin Wright
MATH 118F
Algebra Problem Set
With Solutions
Problem 1: A rental car costs 71.44 per day plus 1.66 per mile. If the total cost is $159.23,
find the number of miles used.
Solution:
Let x = number of miles
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
159.23 = 71.44 + 1.66x
Solving for x:
159.23 - 71.44 = 1.66x
87.79 = 1.66x
x = 87.79 ÷ 1.66
x = 52.9 miles
Mathematical justification:
Check: 71.44 + 1.66(52.9) = 71.44 + 87.81 = 159.25 ✓
Problem 2: A ball is thrown upward from a height of 73 feet with initial velocity 76 ft/s.
Equation: h(t) = -7t² + 76t + 73 When does the ball hit the ground?
Solution:
When the ball hits the ground, h(t) = 0
Setting up the equation:
-7t² + 76t + 73 = 0
Using the quadratic formula: t = (-b ± √(b² - 4ac)) / (2a)
Where a = -7, b = 76, c = 73
t = (-76 ± √(76² - 4(-7)(73))) / (2(-7))
t = (-76 ± √(5776 + 2044)) / -14
t = (-76 ± √7820) / -14
t = (-76 ± 88.43) / -14
Taking the positive solution:
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:45:11 GMT -05:00
https://www.coursehero.com/file/251540570/MTH-230-Algebra-Solutions-1358docx/
, MATH 118F | September 13, 2025
t = (-76 + 88.43) / -14
t = -0.89 seconds
The ball hits the ground after -0.89 seconds.
Problem 3: A plumber charges 82.74 for a service call plus 1.03 per hour of work. If the total
cost is $318.66, find the number of hours used.
Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
318.66 = 82.74 + 1.03x
Solving for x:
318.66 - 82.74 = 1.03x
235.92 = 1.03x
x = 235.92 ÷ 1.03
x = 229.0 hours
Double-checking the work:
Check: 82.74 + 1.03(229.0) = 82.74 + 235.87 = 318.61 ✓
Problem 4: A rental car costs 41.90 per day plus 0.93 per mile. If the total cost is $159.87,
find the number of miles used.
Solution:
Let x = number of miles
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
159.87 = 41.90 + 0.93x
Solving for x:
159.87 - 41.90 = 0.93x
117.97 = 0.93x
x = 117.97 ÷ 0.93
x = 126.8 miles
Verify:
Check: 41.90 + 0.93(126.8) = 41.90 + 117.92 = 159.82 ✓
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:45:11 GMT -05:00
https://www.coursehero.com/file/251540570/MTH-230-Algebra-Solutions-1358docx/
