Let's break down the problem to find the correct equation describing the accountant's fees.
1. Basic Fee: The accountant charges a basic fee of \[tex]$150, regardless of the number of hours worked.
2. Additional Fee per Hour: The accountant charges an additional \$[/tex]25 for each hour of work beyond the basic fee.
To represent this relationship in an algebraic equation, we need to define:
- [tex]\( y \)[/tex] as the total fee charged.
- [tex]\( x \)[/tex] as the number of hours worked in addition to the initial basic fee.
3. Equation Construction:
- The total fee [tex]\( y \)[/tex] includes the basic fee and the fee for the additional hours worked.
- Mathematically, this can be written as:
[tex]\[
y = 150 + 25x
\][/tex]
- Here, 150 is the basic fee, and [tex]\( 25x \)[/tex] represents the additional fee charged at a rate of \[tex]$25 per hour for \( x \) hours worked.
Now, let's examine the given equations to determine which one matches our derived equation:
1. \( y = 150 - 25x \)
This equation suggests the total fee decreases as the number of hours increases, which is incorrect since the fee should increase with more hours.
2. \( y = 150 + 25x \)
This equation correctly incorporates the basic fee of \$[/tex]150 and adds the additional fee of \[tex]$25 per hour.
3. \( y = 25 - 150x \)
This equation is incorrect as it implies a starting fee of \$[/tex]25 with a deduction per hour, which does not reflect the given problem.
4. [tex]\( y = 25 + 150x \)[/tex]
This equation is also incorrect as it suggests a starting fee of \[tex]$25 and an additional fee of \$[/tex]150 per hour, which is not consistent with the problem.
Therefore, the correct equation that describes the accountant's fee structure is:
[tex]\[
y = 150 + 25x
\][/tex]
So, the answer is the second equation:
[tex]\[
y = 150 + 25x
\][/tex]
