- Define the relationship between pay and hours worked as \(P = r \times H\), where \(r\) is the hourly rate.
- Calculate the hourly rate by dividing the total pay by the hours worked for each day: \(r = \frac{P}{H}\).
- Observe that for Day 1, Day 2, and Day 3, the quotient is consistently \(\$9.50\).
- Conclude that Igor's unit rate is \(\boxed{\$9.50}\) per hour.
Explanation
- Analyzing the Relationship Between Pay and Hours
The problem asks for Igor's hourly wage, which is the unit rate of pay. We are given the hours worked and the total pay for three consecutive days. Since the hourly rate is consistent, the unit rate can be determined by dividing the total amount paid by the total number of hours worked for any of the given days. Let \(r\) be the hourly rate in dollars per hour. The relationship between the total pay \(P\) and hours worked \(H\) is given by \(P = r \times H\), which implies \(r = \frac{P}{H}\).
- Calculating the Hourly Rate
Using the data provided for each day, we calculate the hourly rate \(r\):
- For Day 1: \(r = \frac{\$57.00}{6 \text{ hours}} = \$9.50 \text{ per hour}\)
- For Day 2: \(r = \frac{\$85.50}{9 \text{ hours}} = \$9.50 \text{ per hour}\)
- For Day 3: \(r = \frac{\$66.50}{7 \text{ hours}} = \$9.50 \text{ per hour}\)
As expected, the hourly rate is consistent across all three days.
- Conclusion and Final Answer
The calculations confirm that for every hour worked, Igor is paid \(\$9.50\). Therefore, his unit rate is \(\$9.50\) per hour. The final answer is \(\boxed{\$9.50}\).
Examples
Understanding unit rates is essential for managing personal finances and evaluating job offers. For example, if you are offered a part-time job, you can use the total pay and the hours worked to determine your actual hourly rate, which allows you to compare different job opportunities effectively. In this scenario, Igor used his daily earnings to calculate his consistent hourly wage, ensuring he is being paid fairly for his time.