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Question

Difficulty: EasyLinear Equations in One Variable

A plumbing service charges a flat diagnostic fee of $45\$45 plus $65\$65 for each hour of repair work. If the total bill for a repair job was $305\$305, how many hours of repair work were performed?

Answer: 4 hours

Answer

The total number of hours of repair work performed was 4.
To determine the number of repair hours, represent the scenario with the linear equation 45+65h=30545 + 65h = 305, where hh is the number of hours. Subtracting 45 from both sides yields 65h=26065h = 260. Dividing 260 by 65 gives h=4h = 4.

Step-by-Step Solution

1
Formulate the linear equation from the word problem context.
45+65h=30545 + 65h = 305
The total charge consists of a one-time fixed fee of 45plusavariablefeeof45 plus a variable fee of 65 per hour hh.
2
Isolate the variable term by subtracting 45 from both sides of the equation.
65h=26065h = 260
Subtracting the constant fee isolates the total cost incurred from hourly work.
3
Divide both sides by the coefficient of the variable to solve for hh.
h=4h = 4
Dividing the total labor charge (260)bythehourlyrate(260) by the hourly rate ( 65) yields the number of hours worked.

Key Concept

Linear Equations in One Variable
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Topics

Linear Equations in One Variable

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