MATH 280 Algebra Fall2025 Solutions 4295|MTH 145 Algebraic Equations Problem Set With Solutions

MTH 145 | September 13, 2025



Benjamin Gomez
Michelle Martin
MTH 145

Algebraic Equations Problem Set
With Solutions

Problem 1: A plumber charges 67.81 for a service call plus 1.29 per hour of work. If the total
cost is $353.86, find the number of hours used.

Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
353.86 = 67.81 + 1.29x
Solving for x:
353.86 - 67.81 = 1.29x
286.05 = 1.29x
x = 286.05 ÷ 1.29
x = 221.7 hours
Making sure each step follows logically:
Check: 67.81 + 1.29(221.7) = 67.81 + 285.99 = 353.80 ✓



Problem 2: A rental car costs 86.98 per day plus 4.32 per mile. If the total cost is $256.53,
find the number of miles used.

Solution:
Let x = number of miles
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
256.53 = 86.98 + 4.32x
Solving for x:
256.53 - 86.98 = 4.32x
169.55 = 4.32x
x = 169.55 ÷ 4.32
x = 39.2 miles
Direct approach:


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, MTH 145 | September 13, 2025



Check: 86.98 + 4.32(39.2) = 86.98 + 169.34 = 256.32 ✓
Note: I'll need to review this concept before the midterm



Problem 3: A plumber charges 28.56 for a service call plus 5.06 per hour of work. If the total
cost is $320.30, find the number of hours used.

Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
320.30 = 28.56 + 5.06x
Solving for x:
320.30 - 28.56 = 5.06x
291.74 = 5.06x
x = 291.74 ÷ 5.06
x = 57.7 hours
Check:
Check: 28.56 + 5.06(57.7) = 28.56 + 291.96 = 320.52 ✓



Problem 4: A plumber charges 30.40 for a service call plus 3.67 per hour of work. If the total
cost is $361.49, find the number of hours used.

Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
361.49 = 30.40 + 3.67x
Solving for x:
361.49 - 30.40 = 3.67x
331.09 = 3.67x
x = 331.09 ÷ 3.67
x = 90.2 hours
Direct approach:
Check: 30.40 + 3.67(90.2) = 30.40 + 331.03 = 361.43 ✓
Note: This problem connects to what we'll cover next week


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