Desiree works 28 hours per week. She has a monthly income of \( \$ 120 \) from investments. Desiree also plays in a band one night a week making \( \$ 200 \). She has a total annual income of \( \$ 49,696 \). Desiree wants to ask her boss for a raise so that next year she can have a total income of \( \$ 51,880 \). Assuming the other incomes remain the same, how much of an hourly raise will Desiree need? a. \( \$ 1.25 \) b. \( \$ 1.50 \) c. \( \$ 1.75 \) d. \( \$ 2.00 \)

To find out how much of an hourly raise Desiree needs, we first need to calculate her current weekly earnings from her job. 1. **Current Annual Income from Work:** Total current annual income: \( \$ 49,696 \) Income from investments: \( \$ 120 \times 12 = \$ 1,440 \) Income from playing in a band: \( \$ 200 \times 52 = \$ 10,400 \) Therefore, income from her job: \( 49,696 - 1,440 - 10,400 = 37,856 \) 2. **Current Hourly Wage:** She works 28 hours per week, which is \( 28 \times 52 = 1,456 \) hours annually. Current hourly wage = \( \frac{37,856}{1,456} \approx 26.00 \) per hour. 3. **Required Total Income Next Year:** Desiree wants a total annual income of \( \$ 51,880 \). Subtracting other income sources: \( 51,880 - 1,440 - 10,400 = 40,040 \) is how much she needs to earn from her job next year. 4. **Hourly Raise Calculation:** To find the required total hours worked (in hours) for next year: Required hourly wage = \( \frac{40,040}{1,456} \approx 27.50 \) per hour. Therefore, the raise per hour = \( 27.50 - 26.00 = 1.50 \). So, the required hourly raise for Desiree is \( \$ 1.50 \), which corresponds to option **b.** If you want to check your own calculations, make sure to break down each income source and ensure you account for total hours worked properly! And always subscribe to the logic of systematic assumptions—think it through step-by-step!