To determine whether Jace's earnings are proportional to the number of hours that he works, we need to check if the ratio of earnings to hours is constant for each dataset. Here's the step-by-step solution:
1. Identify the data points:
- For 1 hour of work, Jace earns \[tex]$20.
- For 2 hours of work, Jace earns \$[/tex]30.
- For 3 hours of work, Jace earns \[tex]$40.
2. Calculate the ratio of earnings to hours for each data point:
- For 1 hour of work: \(\frac{\$[/tex]20}{1 \text{ hour}}\) = 20.0
- For 2 hours of work: [tex]\(\frac{\$30}{2 \text{ hours}}\)[/tex] = 15.0
- For 3 hours of work: [tex]\(\frac{\$40}{3 \text{ hours}}\)[/tex] ≈ 13.33 (approximately)
3. List the calculated ratios:
- Ratio for 1 hour: 20.0
- Ratio for 2 hours: 15.0
- Ratio for 3 hours: 13.33
4. Compare the ratios:
- The calculated ratios are 20.0, 15.0, and 13.33.
5. Check for consistency:
- Since the ratios 20.0, 15.0, and 13.33 are not equal, the ratios are not constant.
6. Conclusion:
- Because the ratios of earnings to hours are not the same, Jace's earnings are not proportional to the number of hours that he works.
In summary, Jace's earnings are not proportional to the number of hours that he works, as evidenced by the varying ratios of earnings to hours.
