Answer :
To determine which equation accurately represents the scenario where an accountant charges a base fee of [tex]$120 and an additional $[/tex]40 per hour to complete a company's taxes, we can follow these logical steps:
1. Identify the variables:
- Let \( y \) represent the total fee charged by the accountant.
- Let \( x \) represent the number of hours the accountant works.
2. Understand the charges:
- The accountant charges a fixed base fee of $120.
- In addition to the base fee, the accountant charges $40 for each hour worked.
3. Formulate the equation:
- The total fee \( y \) consists of the base fee plus the additional fee for the hours worked:
- Mathematically, this can be expressed as:
[tex]\[ y = \text{base fee} + (\text{additional fee per hour} \times \text{number of hours}) \][/tex]
Substituting the given values:
[tex]\[ y = 120 + 40x \][/tex]
4. Verify the options:
- Option 1: \( y = 40 + 120x \)
- This option suggests that the base fee is [tex]$40 and the additional fee per hour is $[/tex]120, which is incorrect.
- Option 2: \( y = 40 - 120x \)
- This option suggests a fee reduction as hours increase, which is incorrect.
- Option 3: \( y = 120 + 40x \)
- This option correctly represents the scenario with a base fee of [tex]$120 and an additional $[/tex]40 per hour.
- Option 4: \( y = 120 - 40x \)
- This option suggests that the total fee decreases as hours increase, which is incorrect.
Thus, the correct equation that can be used to describe this problem is \( y = 120 + 40x \). The answer is:
\(
\boxed{y = 120 + 40x}
\)
Therefore, the correct answer choice is:
[tex]\[ \boxed{3} \][/tex]
1. Identify the variables:
- Let \( y \) represent the total fee charged by the accountant.
- Let \( x \) represent the number of hours the accountant works.
2. Understand the charges:
- The accountant charges a fixed base fee of $120.
- In addition to the base fee, the accountant charges $40 for each hour worked.
3. Formulate the equation:
- The total fee \( y \) consists of the base fee plus the additional fee for the hours worked:
- Mathematically, this can be expressed as:
[tex]\[ y = \text{base fee} + (\text{additional fee per hour} \times \text{number of hours}) \][/tex]
Substituting the given values:
[tex]\[ y = 120 + 40x \][/tex]
4. Verify the options:
- Option 1: \( y = 40 + 120x \)
- This option suggests that the base fee is [tex]$40 and the additional fee per hour is $[/tex]120, which is incorrect.
- Option 2: \( y = 40 - 120x \)
- This option suggests a fee reduction as hours increase, which is incorrect.
- Option 3: \( y = 120 + 40x \)
- This option correctly represents the scenario with a base fee of [tex]$120 and an additional $[/tex]40 per hour.
- Option 4: \( y = 120 - 40x \)
- This option suggests that the total fee decreases as hours increase, which is incorrect.
Thus, the correct equation that can be used to describe this problem is \( y = 120 + 40x \). The answer is:
\(
\boxed{y = 120 + 40x}
\)
Therefore, the correct answer choice is:
[tex]\[ \boxed{3} \][/tex]
