Answer :
Let's examine the problem step by step.
1. Flat Fee: The HVAC technician charges a flat fee of [tex]$150 just for inspecting the air conditioning system. This is a one-time charge that applies regardless of the number of hours worked.
2. Hourly Rate for Repairs: If the customer decides to proceed with the repair, the technician charges an additional $[/tex]75 for each hour of labor. This means for every hour the technician works, the total cost increases by [tex]$75.
3. Total Cost Calculation: To determine the total cost \( C \) of the repair, we need to consider both the flat fee and the hourly rate. Let \( t \) represent the number of hours the technician works on the repair.
4. Equation Setup:
- The flat fee is $[/tex]150.
- The hourly cost for \`t\` hours of repair work is $75 times [tex]\( t \)[/tex], or [tex]\( 75t \)[/tex].
Thus, the total cost [tex]\( C \)[/tex] is the sum of the flat fee and the hourly charges. Therefore, the equation that describes the total cost [tex]\( C \)[/tex] in terms of the number of hours [tex]\( t \)[/tex] is:
[tex]\[ C = 75t + 150 \][/tex]
This means the correct equation is [tex]\( C = 75t + 150 \)[/tex].
1. Flat Fee: The HVAC technician charges a flat fee of [tex]$150 just for inspecting the air conditioning system. This is a one-time charge that applies regardless of the number of hours worked.
2. Hourly Rate for Repairs: If the customer decides to proceed with the repair, the technician charges an additional $[/tex]75 for each hour of labor. This means for every hour the technician works, the total cost increases by [tex]$75.
3. Total Cost Calculation: To determine the total cost \( C \) of the repair, we need to consider both the flat fee and the hourly rate. Let \( t \) represent the number of hours the technician works on the repair.
4. Equation Setup:
- The flat fee is $[/tex]150.
- The hourly cost for \`t\` hours of repair work is $75 times [tex]\( t \)[/tex], or [tex]\( 75t \)[/tex].
Thus, the total cost [tex]\( C \)[/tex] is the sum of the flat fee and the hourly charges. Therefore, the equation that describes the total cost [tex]\( C \)[/tex] in terms of the number of hours [tex]\( t \)[/tex] is:
[tex]\[ C = 75t + 150 \][/tex]
This means the correct equation is [tex]\( C = 75t + 150 \)[/tex].
