Math Problem Statement

A company pays $20 per hour for up to 5 hours of work, and $30 per hour for overtime hours (hours beyond 5). If x is the total hours worked, and more than 5 hours have been worked, what is the expression for just the overtime hours worked?

Solution

The question asks for the expression that represents just the overtime hours worked. Here's how we can break it down:

  1. The total hours worked is given as xx.
  2. Regular work is for up to 5 hours, so any hours beyond 5 are considered overtime.
  3. Therefore, the number of overtime hours is x5x - 5, provided that x>5x > 5.

Final Answer:

The expression for the overtime hours is: x5x - 5

Would you like me to explain this further or solve any additional parts of the question? Let me know!


Here are 5 related questions for practice:

  1. If someone worked 8 hours, how many overtime hours would they have worked?
  2. What would the total payment be if x=10x = 10 total hours worked?
  3. If the company increases overtime pay to $40/hour, how would the overtime cost expression change?
  4. How can you write the total pay expression for both regular and overtime hours combined?
  5. What happens if someone works exactly 5 hours—how many overtime hours would they have?

Quick Tip:

Always identify the breakpoint in word problems like these (in this case, 5 hours). This will help you clearly separate the scenarios and write the correct expressions!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Expressions
Piecewise Functions

Formulas

Overtime hours = Total hours - 5 (if Total hours > 5)

Theorems

Linear relationships in algebra

Suitable Grade Level

Grades 7-9