The table below shows Andres's earnings on the job.

Question

Time left parenthesis hours right parenthesisTime (hours) Earnings left parenthesis dollars right parenthesisEarnings (dollars)
1313 dollar sign, 387, point, 4, 0$387.40
1717 dollar sign, 506, point, 6, 0$506.60
3030 dollar sign, 894$894
If e represents his total earnings in dollars and cents for any number of hours worked, h, write a proportional equation for e in terms of h that matches the context.

Answer 1

To create a proportional equation for Andres's total earnings \( e \) in terms of hours worked \( h \), we can first analyze the provided data points:

1. For 13 hours, \( e = 387.40 \)
2. For 17 hours, \( e = 506.60 \)
3. For 30 hours, \( e = 894 \)

Next, we can find the earnings per hour for the points provided.

Step 1: Calculate earnings per hour

1. For 13 hours: \[ \text{Earnings per hour} = \frac{387.40}{13} \approx 29.80 \]

2. For 17 hours: \[ \text{Earnings per hour} = \frac{506.60}{17} \approx 29.80 \]

3. For 30 hours: \[ \text{Earnings per hour} = \frac{894}{30} \approx 29.80 \]

Step 2: Determine the proportional relationship

From the calculations, we see that Andres's earnings per hour are consistent at approximately $29.80 per hour.

Step 3: Write the proportional equation

The proportional equation relating total earnings \( e \) to hours worked \( h \) can be written as: \[ e = 29.80h \]

Final Equation

Thus, the proportional equation for Andres's total earnings in terms of hours worked is: \[ e = 29.80h \]