Math Problem Statement

Calculate the gross pay for an employee who worked 50.75 hours in a week, given a regular hourly rate of $17.70, with overtime pay for hours beyond 40 at 1.5 times the regular rate.

Solution

Let’s solve the problem step by step:

Given:

  1. Regular hourly rate: $17.70/hour
  2. Total hours worked: 50.75 hours
  3. Overtime threshold: 40 hours/week
  4. Overtime pay rate: 1.5 times the regular hourly rate

Calculations:

  1. Regular Pay Amount:

    • Regular hours: 40 hours
    • Regular pay = Regular hours × Hourly rate
      = 40×17.70=708.0040 \times 17.70 = 708.00
  2. Overtime Pay:

    • Overtime hours: 50.7540=10.7550.75 - 40 = 10.75 hours
    • Overtime pay rate: 17.70×1.5=26.5517.70 \times 1.5 = 26.55 per hour
    • Overtime pay = Overtime hours × Overtime rate
      = 10.75×26.55=285.4110.75 \times 26.55 = 285.41
  3. Gross Pay:

    • Gross pay = Regular pay + Overtime pay
      = 708.00+285.41=993.41708.00 + 285.41 = 993.41

Final Answers:

  1. Regular pay amount: $708.00
  2. Overtime pay: $285.41
  3. Gross pay: $993.41

Let me know if you’d like further clarifications or have additional questions!


Related Questions:

  1. How would the gross pay change if the overtime rate was doubled instead of 1.5 times?
  2. What if Alice worked 60 hours instead of 50.75 hours—how would her gross pay change?
  3. How is overtime calculated for different industries, and are there any standard legal guidelines?
  4. What would happen if Alice’s hourly rate increased by 10%?
  5. How do state-specific overtime rules affect pay calculations?

Tip: Always double-check your overtime calculations when hours worked exceed the threshold, as errors can significantly impact payroll processing!

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Basic Algebra
Payroll Calculations

Formulas

Regular Pay = Regular Hours × Hourly Rate
Overtime Pay = Overtime Hours × Overtime Rate
Gross Pay = Regular Pay + Overtime Pay

Theorems

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Suitable Grade Level

High School