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Automotive Mechanic Billing Solution: Find Fixed Fee & Hourly Rate

Solve the system of equations to determine the fixed fee and hourly rate of an auto mechanic based on billing information from two car repairs. The fixed fee is $50 and the hourly rate is $20.

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Automotive Mechanic Billing Solution: Find Fixed Fee & Hourly Rate

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  1. Solving A System of Equations Joseph Mares and Cesar Moreno December 19, 2013 5B

  2. Problem Situation • An auto mechanic charges a fixed fee for examining a vehicle for engine problems plus an hourly rate for repairing the engine. The mechanic worked for 6 hours on a car with engine problems and the bill totaled $170. The mechanic worked on another car with engine problems for 4 hours, and the bill totaled $130. • Find the fixed fee and the hourly rate.

  3. Define Variables • F is the fixed rate fee, and x is the hourly rate.

  4. System of Equations • F + 6x = $170 • F + 4x= $130

  5. Solution Method • We are going to solve it by elimination.

  6. Steps of Solution • F + 6x = $170 Eliminate the F by subtracting F + 4x= $130 the equations. • 2x = $ 40 • Divide both sides by 2. • x = $ 20 • Use 20 in the first equation. • F + 6(20) = 170 Multiply and then subtract. • F + 120 = 170 F = 50

  7. Solution to the System of Equations (50,20)

  8. Check of Solution • 50 + 4*20 = 130 ☺ • 50 + 6*20 = 170 ☺

  9. Solution in the Problem Situation • $50 is the fixed rate fee and $20is the hourly rate.

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