To solve this, let's commence by setting up a function that illustrates the arithmetic sequence that gives the cost of the service based on the hours of work.
The repair service has a fixed fee to visit your home, which is $55. Then, they also charge an hourly rate of $24.50 for the work they perform. Therefore, the total cost, C(n), is given by the function:
C(n) = service_fee + hourly_rate * n
where
- n is the number of hours of work,
- service_fee is the fixed fee to visit your home, and
- hourly_rate is the rate they charge for an hour of work.
Here, service_fee is $55 and hourly_rate is $24.50.
Now, we can find out the total cost for a 7-hour job by substituting n = 7 into our cost function.
C(7) = service_fee + hourly_rate * 7
Substituting the known values:
C(7) = $55 + $24.5 * 7
So, the total cost for a 7-hour job would be $226.5. That’s how much it would cost to use this repair service for 7 hours.