An electrician charges a set fee of $100 for every house call and then charges an additional hourly rate. One day, the electrician earned a total of $250 for a 2-hour job. Write an equation for the function C(t), representing the total cost of the electrician's services if the electrician spends two hours in the house working.

Let's break down the question step by step. The electrician has two components to the pricing structure.

A set fee of $100 for every house call, regardless of the time spent working and An additional hourly rate for the actual time spent working.

 We're told that for a 2-hour job, the electrician earned a total of $250. We can use this information to determine the additional hourly rate.

We deduct the set fee from the total earnings to find out how much the electrician made from the hourly rate.

So We Have, Total earnings for 2 hours = $250 and Set fee = $100.

Earning For Hourly = $250 - $100

Earning For Hourly = $150.

$150 is for 2 hours of work, we divide by 2 to find the hourly rate.

= $150/2

= $ 75 Per Hour.

 We have all the information needed to write the equation for the total cost of the electrician's services, C(t), where t is the number of hours spent working.

C(t) = Set fee + (Hourly rate × t) C(t) = $100 + ($75 × t)

So, for a 2-hour job, substituting t with 2.

C(2) = $100 + ($75 × 2)

C(2) = $100 + $150

C(2) = $250.

So, the function representing the total cost C(t) of the electrician's services for t hours of work is C(t) = $100 + $75t .