Question
A repair service charges $60.00 to come to your home plus $20.50 per hour. Find a function that describes the arithmetic sequence. Then find the total cost for a 7-hour job.
Answers
GPT-4o mini
To describe the total cost as a function of hours worked, we can define the function \( C(h) \), where \( h \) is the number of hours worked. The total cost consists of two parts: a fixed service charge of $60.00 and a variable charge of $20.50 per hour.
The function can be expressed as:
\[
C(h) = 60 + 20.50h
\]
Now, to find the total cost for a 7-hour job, we will substitute \( h = 7 \) into the function:
\[
C(7) = 60 + 20.50 \times 7
\]
Calculating the hourly charge:
\[
20.50 \times 7 = 143.50
\]
Now, add this to the fixed service charge:
\[
C(7) = 60 + 143.50 = 203.50
\]
Therefore, the total cost for a 7-hour job is:
\[
\boxed{203.50}
\]
The function can be expressed as:
\[
C(h) = 60 + 20.50h
\]
Now, to find the total cost for a 7-hour job, we will substitute \( h = 7 \) into the function:
\[
C(7) = 60 + 20.50 \times 7
\]
Calculating the hourly charge:
\[
20.50 \times 7 = 143.50
\]
Now, add this to the fixed service charge:
\[
C(7) = 60 + 143.50 = 203.50
\]
Therefore, the total cost for a 7-hour job is:
\[
\boxed{203.50}
\]