ophia 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?

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Answer 1

To solve the problem, we'll break it down into the three parts as requested.

Part A:

We need to compare the two pay increases: 12% of her current salary and a flat $4,000 increase.

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

2. Compare the two increase options:

   • 12% increase: $4,488
   • Flat increase: $4,000

Since $4,488 (the 12% increase) is greater than $4,000, Sophia should choose the 12% increase.

Part B:

Now, we calculate her new annual salary based on the 12% increase: \[ \text{New Salary} = \text{Current Salary} + \text{12% increase} = 37,400 + 4,488 = 41,888 \]

Next, we calculate her hourly wage:

1. Total hours worked in a year: \[ \text{Total hours} = 42 \text{ hours/week} \times 50 \text{ weeks} = 2,100 \text{ hours} \]

2. Hourly wage: \[ \text{Hourly Wage} = \frac{\text{New Salary}}{\text{Total hours}} = \frac{41,888}{2,100} \approx 19.95 \]

So, Sophia's hourly wage will be approximately $19.95.

Part C:

Now we compare Sophia's current job with the new job based on hourly rates.

1. Current job hourly rate:
   From Part B, we've calculated it as approximately $19.95.

2. New job's salary and hourly rate calculation:

   • New Salary = $52,900
   • Total hours worked in a year (for new job): \[ \text{Total hours} = 55 \text{ hours/week} \times 50 \text{ weeks} = 2,750 \text{ hours} \]

3. New job's hourly rate: \[ \text{Hourly Wage} = \frac{52,900}{2,750} \approx 19.18 \]

Deciding Based on Hourly Rate:

• Current job hourly rate: $19.95
• New job hourly rate: $19.18

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