Question: 5

Question

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.

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.)

Answer 1

Part A:

To determine whether Sophia should choose the 12% higher salary or the $4,000 increase, we need to calculate both options based on her current salary of $37,400.

1. Calculating the 12% increase: \[ 0.12 \times 37,400 = 4,488 \] \[ \text{New salary with 12% increase} = 37,400 + 4,488 = 41,888 \]

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

Now we compare the two new salaries:

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

Since $41,888 (12% increase) is greater than $41,400 ($4,000 increase), Sophia should choose the 12% increase.

Part B:

Now we need to calculate Sophia's hourly wage if she chooses the 12% pay bump.

1. Calculate total hours worked for the year: \[ \text{Total hours} = \text{hours per week} \times \text{weeks per year} = 42 \times 50 = 2,100 \text{ hours} \]

2. Calculate her hourly wage with the new salary: \[ \text{Hourly wage} = \frac{\text{New salary}}{\text{Total hours}} = \frac{41,888}{2,100} \] \[ \text{Hourly wage} \approx 19.97 \]

Therefore, rounding to the nearest cent, Sophia's hourly wage will be $19.97 if she chooses the higher pay bump (12% increase).