Sophia currently makes $37,400 per year. Her employer offered her additional responsibilities that will allow her to make either 12% of her salary more per year or $4,000 more per year.

Question

Part A:
Should Sophia choose to make 12% of her salary more per year or $4,000 more per year?

Part B:
Including the time spent on Sophia's additional responsibilities, she will be working 42 hours per week. If she works for 50 weeks during the year, how much will she make per hour if she chooses the higher pay bump in Part A? (Round your answer to the nearest cent.)

Part C:
Sophia is offered a new job that will require 55 hours of work for 50 weeks a year, but will earn her a salary of $52,900. Based strictly on the hourly rate, should Sophia continue at her current job, or take the new job?

Answer 1

Let's solve each part step by step.

Part A:

To determine whether Sophia should choose the 12% increase or the $4,000 increase, we first need to calculate the amount of each option.

1. Calculate the 12% increase in salary: \[ \text{12% increase} = 0.12 \times 37,400 = 4,488 \] Therefore, if Sophia chooses this option, her new salary would be: \[ \text{New Salary} = 37,400 + 4,488 = 41,888 \]

2. Compare it with the $4,000 increase: Adding $4,000 to her current salary gives: \[ \text{New Salary} = 37,400 + 4,000 = 41,400 \]

3. Determine which option is better:

   • 12% increase salary: $41,888
   • $4,000 increase salary: $41,400

Since $41,888 is greater than $41,400, Sophia should choose the 12% increase.

Part B:

Now we need to calculate how much Sophia will make per hour if she chooses the higher pay bump.

1. Calculate her annual salary from the raised salary: \[ \text{New Salary} = 41,888 \]

2. Calculate total hours worked in the year: \[ \text{Hours per week} = 42 \quad \text{and} \quad \text{Weeks per year} = 50 \] \[ \text{Total hours} = 42 \times 50 = 2,100 \text{ hours} \]

3. Calculate her hourly rate: \[ \text{Hourly rate} = \frac{\text{Annual Salary}}{\text{Total hours}} = \frac{41,888}{2,100} \approx 19.95 \]

So, rounding this to the nearest cent, Sophia will make approximately $19.95 per hour.

Part C:

Now we will evaluate whether Sophia should continue at her current job or take the new job based on the hourly rate.

1. Calculate the hourly rate of the new job: New job salary: $52,900 \[ \text{Total hours for new job} = 55 \times 50 = 2,750 \text{ hours} \] \[ \text{Hourly rate (new job)} = \frac{52,900}{2,750} \approx 19.18 \]

2. Comparison of hourly rates:

   • Current Job Hourly Rate: $19.95
   • New Job Hourly Rate: $19.18

Since $19.95 (current job) is greater than $19.18 (new job), Sophia should continue at her current job based strictly on the hourly rate.

Summary of Answers:

• Part A: Choose 12% increase.
• Part B: $19.95 per hour.
• Part C: Continue at her current job.