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

To answer the questions, we will perform the necessary calculations step by step.

Part A: Choosing the Pay Increase

1. Calculating 12% of her current salary: \[ \text{12% increase} = 0.12 \times 37,400 = 4,488 \]

2. Calculating Sophia's new salary with the 12% increase: \[ \text{New Salary} = 37,400 + 4,488 = 41,888 \]

3. Calculating her salary with the $4,000 increase: \[ \text{New Salary with $4,000} = 37,400 + 4,000 = 41,400 \]

4. Comparison:

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

Since the 12% increase results in a higher salary, Sophia should choose the 12% increase.

Part B: Calculating Hourly Rate with 12% Increase

1. Total Annual Hours: \[ \text{Total Hours} = 42 \text{ hours/week} \times 50 \text{ weeks} = 2,100 \text{ hours} \]

2. Calculating Hourly Rate with the new salary from the 12% increase: \[ \text{Hourly Rate} = \frac{41,888}{2,100} \approx 19.97333 \]

3. Rounding to the nearest cent: \[ \text{Hourly Rate} \approx 19.97 \]

Thus, if she chooses the higher pay bump, her hourly rate will be approximately $19.97.

Part C: Comparing Hourly Rates with New Job Offer

1. Calculating Total Annual Hours for the new job: \[ \text{Total Hours for new job} = 55\text{ hours/week} \times 50 \text{ weeks} = 2,750 \text{ hours} \]

2. Calculating Hourly Rate for the new job: \[ \text{Hourly Rate for new job} = \frac{52,900}{2,750} \approx 19.21818 \]

3. Rounding to the nearest cent: \[ \text{Hourly Rate for new job} \approx 19.22 \]

Comparison

• Current job hourly rate (with 12% increase): $19.97
• New job hourly rate: $19.22

Since $19.97 (current job) > $19.22 (new job), Sophia should continue at her current job.