Question

Lloyd normally works 7.5 hours per day and earns \$4.50 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?

• A. \$33.75
• B. \$47.25
• C. \$51.75
• D. \$54.00
• E. \$70.00

Hint:

In wage calculation problems, always break down the hours into 'regular' and 'overtime' first. Calculate the pay for each part separately before adding them together to avoid errors. Be careful with multipliers like "1.5 times his regular rate".

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This problem requires calculating total earnings based on regular hours and overtime hours, where overtime is paid at a higher rate. We need to separate the total hours worked into these two categories.
Step 2: Key Formula or Approach:
Total Earnings = (Regular Hours \(\times\) Regular Rate) + (Overtime Hours \(\times\) Overtime Rate)
First, we need to calculate the overtime rate and the number of overtime hours.
Step 3: Detailed Explanation:
1. Identify the given information:
- Regular work day: 7.5 hours
- Regular hourly rate: \$4.50 per hour
- Overtime multiplier: 1.5 times the regular rate
- Total hours worked: 10.5 hours
2. Calculate the overtime hours:
Overtime Hours = Total Hours Worked - Regular Hours
\[ \text{Overtime Hours} = 10.5 - 7.5 = 3 \text{ hours} \] 3. Calculate the overtime rate:
Overtime Rate = Regular Rate \(\times\) 1.5
\[ \text{Overtime Rate} = \$4.50 \times 1.5 = \$6.75 \text{ per hour} \] 4. Calculate the earnings for regular hours:
Regular Earnings = Regular Hours \(\times\) Regular Rate
\[ \text{Regular Earnings} = 7.5 \times \$4.50 = \$33.75 \] 5. Calculate the earnings for overtime hours:
Overtime Earnings = Overtime Hours \(\times\) Overtime Rate
\[ \text{Overtime Earnings} = 3 \times \$6.75 = \$20.25 \] 6. Calculate the total earnings for the day:
Total Earnings = Regular Earnings + Overtime Earnings
\[ \text{Total Earnings} = \$33.75 + \$20.25 = \$54.00 \] Step 4: Final Answer:
Lloyd earns \$54.00 for that day. This corresponds to option (D).