Malia works at a movie theater and is paid hourly. One month, she earned $388.80. The total amount she earns can be found using the equation y = 8.1x, where x is the number of hours she works and y is the total amount she earns in dollars.

Question

Bill works at a golf course and is also paid hourly. This table shows the total amount he is paid for different numbers of hours worked.

How do the unit rates compare?

Number of hours
18
28
35

Total amount earned

$144.90
$225.40
$281.75

Answer 1

To compare the unit rates of Malia and Bill, we'll first calculate the hourly wage for both.

Malia's Earnings

The equation representing Malia's earnings is: \[ y = 8.1x \] This means she earns $8.10 for each hour worked.

Unit Rate for Malia:

• \( \text{Unit Rate} = 8.1 \) dollars/hour.

Bill's Earnings

We need to determine Bill's hourly wage from the table of earnings.

Total Amounts for Bill:

• For 18 hours: $144.90
• For 28 hours: $225.40
• For 35 hours: $281.75

We will calculate the hourly wage for each of the hours listed.

1. For 18 hours: \[ \text{Hourly Wage} = \frac{144.90}{18} \approx 8.05 \text{ dollars/hour} \]

2. For 28 hours: \[ \text{Hourly Wage} = \frac{225.40}{28} \approx 8.05 \text{ dollars/hour} \]

3. For 35 hours: \[ \text{Hourly Wage} = \frac{281.75}{35} \approx 8.05 \text{ dollars/hour} \]

Summary of Unit Rates

• Malia's unit rate: \( 8.10 \) dollars/hour
• Bill's unit rate: \( \approx 8.05 \) dollars/hour

Conclusion

Comparing the two unit rates:

• Malia earns \( 8.10 \) dollars/hour.
• Bill earns \( 8.05 \) dollars/hour.

Thus, Malia earns slightly more per hour than Bill.