Question

A contractor has two choices for billing a completed job.
· $500 flat rate, regardless of the number of hours worked
· $20 per hour worked
The graph shows the relationship between pay per hour and number of hours worked for both scenarios.
mc029-1.jpg
What is the solution to this system of equations, and what does it mean to the contractor?
The solution (0, 20) tells the contractor the minimum amount that can be charged.
The solution (0, 500) tells the contractor the maximum amount that can be charged.
The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.
The solution (20, 25) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.

Answer 1

Answer: The solution is (25, 20).

Reason: For the flat rate the pay per hour is 500/h, and the hourly plan pays 20 per hour. Solve 500/h = 20 → h = 25, giving pay per hour = $20. So at 25 hours both billing options give $20/hour (and the flat total is $500). For jobs shorter than 25 hours the $500 flat pays more per hour; for jobs longer than 25 hours the $20/hour option pays more total.