Math Problem Statement

For the first week of November, Kevin Evans worked 48 hours. Kevin earns $9.50 an hour. His employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours. Calculate the following: 1. Regular pay amount, 2. Overtime pay, 3. Gross pay.

Solution

Let’s break this problem down step by step:

Problem Breakdown:

  1. Regular Pay: Kevin worked 48 hours in total, but only the first 40 hours count as "regular time." His hourly pay is $9.50.

    • Regular pay = 40hours×9.50per hour40 \, \text{hours} \times 9.50 \, \text{per hour}.
  2. Overtime Pay: Kevin worked 4840=848 - 40 = 8 overtime hours. Overtime is paid at 1.5×hourly rate1.5 \times \text{hourly rate}.

    • Overtime hourly rate = 1.5×9.50=14.251.5 \times 9.50 = 14.25.
    • Overtime pay = 8hours×14.25per hour8 \, \text{hours} \times 14.25 \, \text{per hour}.
  3. Gross Pay: The gross pay is the sum of the regular pay and the overtime pay:

    • Gross pay = Regular pay + Overtime pay.

Calculations:

  1. Regular pay = 40×9.50=380.0040 \times 9.50 = 380.00.
  2. Overtime pay = 8×14.25=114.008 \times 14.25 = 114.00.
  3. Gross pay = 380.00+114.00=494.00380.00 + 114.00 = 494.00.

Final Answers:

  1. Regular pay amount: $380.00
  2. Overtime pay: $114.00
  3. Gross pay: $494.00

Would you like a detailed explanation for any specific part? Let me know!


Follow-up Questions:

  1. How would the pay change if the overtime rate was doubled instead of 1.5 times the hourly rate?
  2. What would the gross pay be if Kevin worked only 40 hours with no overtime?
  3. How can we calculate Kevin's average hourly earnings for this week (including overtime)?
  4. What if Kevin worked 55 hours instead? How would the pay be affected?
  5. If the hourly rate increased to $12.00, how would his gross pay change for the same 48-hour week?

Tip:

Always keep track of how many hours are overtime versus regular hours, especially when different rates apply.

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Math Problem Analysis

Mathematical Concepts

Basic Arithmetic
Multiplication
Addition
Overtime Calculation

Formulas

Regular pay = Regular hours × Hourly rate
Overtime pay = Overtime hours × (1.5 × Hourly rate)
Gross pay = Regular pay + Overtime pay

Theorems

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Suitable Grade Level

Grades 6-8