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 to make 12% more or $4,000 more, we first need to calculate both options.

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

2. $4,000 increase:
   This is straightforward, as it is already given.

Now, we compare the two increases:

• Increase from 12%: $4,488
• Increase from $4,000: $4,000

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

Part B:

Now, let's find out how much Sophia will make per hour if she chooses the 12% pay bump.

1. New annual salary: \[ \text{New salary} = 37,400 + 4,488 = 41,888 \]

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

3. Hourly rate: \[ \text{Hourly rate} = \frac{41,888}{2,100} \approx 19.96 \]

So, rounding to the nearest cent, Sophia will make approximately $19.96 per hour if she chooses the higher pay bump.

Part C:

Now, let's compare her current job (after the increase) with the new job.

1. Sophia's increased hourly wage from Part B:
   \[ \text{Current hourly rate} = 19.96 \]

2. New job's salary: $52,900.

3. New job's weekly hours: \[ \text{Total hours} = 55 \text{ hours/week} \times 50 \text{ weeks} = 2,750 \text{ hours} \]

4. New job's hourly wage: \[ \text{New hourly rate} = \frac{52,900}{2,750} \approx 19.27 \]

Comparison:

• Current job's hourly rate: $19.96
• New job's hourly rate: $19.27

Since $19.96 (current job) is greater than $19.27 (new job), Sophia should continue at her current job based strictly on the hourly rate.