Math Problem Statement

As the payroll manager for a particular company, your task is to complete the following weekly payroll record. The company pays overtime for all hours worked over 40 at the rate of time-and-a-half. Round to the nearest cent when necessary. Note: Do not round the hourly overtime rate before finding the amount of overtime pay. Employee Sands M 6 T 5 W 10 T 8 F 10 S 6 S 0 Hourly Rate $9.90 Total Hours hr Overtime Hours hr Regular Pay $ Overtime Pay $ Total Pay $

Solution

To complete the weekly payroll record, follow these steps:

Step 1: Calculate Total Hours Worked

Add the hours worked for each day: 6+5+10+8+10+6+0=45hours6 + 5 + 10 + 8 + 10 + 6 + 0 = 45 \, \text{hours}

Step 2: Calculate Overtime Hours

Overtime applies for hours worked beyond 40. Subtract 40 from the total hours: 4540=5overtime hours45 - 40 = 5 \, \text{overtime hours}

Step 3: Calculate Regular Pay

Regular pay covers the first 40 hours at the hourly rate. Multiply the hourly rate by 40: 40×9.90=396.00dollars40 \times 9.90 = 396.00 \, \text{dollars}

Step 4: Calculate Overtime Pay

The overtime rate is time-and-a-half, or 1.5×hourly rate1.5 \times \text{hourly rate}. Compute the overtime rate: 1.5×9.90=14.85dollars per hour1.5 \times 9.90 = 14.85 \, \text{dollars per hour}

Multiply the overtime rate by the overtime hours: 5×14.85=74.25dollars5 \times 14.85 = 74.25 \, \text{dollars}

Step 5: Calculate Total Pay

Add the regular pay and overtime pay: 396.00+74.25=470.25dollars396.00 + 74.25 = 470.25 \, \text{dollars}

Final Payroll Record:

EmployeeTotal Hours (hr)Overtime Hours (hr)Regular Pay ($)Overtime Pay ($)Total Pay ($)
Sands455396.0074.25470.25

Would you like a detailed breakdown of the calculations or further assistance? Here are five related questions for you:

  1. What if the hourly rate increased to $10.50—how would the payroll change?
  2. How would payroll calculations differ if there were bonuses?
  3. Could you calculate payroll for multiple employees using similar parameters?
  4. What tax deductions should be considered for this payroll?
  5. How do you calculate holiday pay for employees?

Tip: Always verify the accuracy of overtime calculations and ensure payroll complies with labor laws.

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Math Problem Analysis

Mathematical Concepts

Basic Arithmetic
Time-and-a-Half Overtime Pay
Payroll Calculation

Formulas

Total Hours = sum of hours worked for each day
Overtime Hours = Total Hours - 40
Regular Pay = hourly rate * 40
Overtime Pay = overtime hours * overtime hourly rate
Total Pay = Regular Pay + Overtime Pay

Theorems

Time-and-a-Half Overtime Pay Calculation

Suitable Grade Level

Grades 9-11