Let's analyze the problem step-by-step and determine which equation correctly represents the charges from the architect.
1. Identify the given values:
- Service charge: \[tex]$75
- Rate per hour: \$[/tex]25
- Total bill: \[tex]$150
- \(h\) represents the number of hours worked.
2. Based on the problem, the total cost can be described as a sum of the service charge and the hourly charges.
3. Let's construct the equation step-by-step:
- The service charge is a fixed amount: \$[/tex]75.
- The hourly charge is dependent on the number of hours worked, which is given by [tex]\(25 \cdot h\)[/tex].
4. Combining these, the total bill is made up of the service charge plus the hourly charges:
- Service charge + (Rate per hour [tex]\(\cdot\)[/tex] Hours)
- \[tex]$75 + \$[/tex]25 [tex]\(\cdot\)[/tex] [tex]\(h\)[/tex]
5. Set this expression equal to the total bill (\$150):
- [tex]\(75 + 25h = 150\)[/tex]
6. Examine the provided options to find the matching equation:
- [tex]\(75 + 25h = 150\)[/tex]
- [tex]\(25 + 75h = 150\)[/tex]
- [tex]\(75(h + 25) = 150\)[/tex]
- [tex]\(25(h + 75) = 150\)[/tex]
7. The correct equation that accurately represents the charges based on the given information is:
- [tex]\(75 + 25h = 150\)[/tex]
Thus, the correct answer is the first option:
[tex]\[
75 + 25h = 150
\][/tex]
