To determine which proportional relationship has the greater rate of change, we need to establish both the rate of change for Jamie and for Ashley's scenarios.
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Jamie's Rate of Change:
- Jamie finished a certain number of questions in 20 minutes. We need to interpret this as a ratio.
- Let’s say Jamie finishes Q questions in 20 minutes: \[ \text{Rate of change (R)} = \frac{\text{Change in y (questions)}}{\text{Change in x (minutes)}} = \frac{Q}{20} \]
- Without a specific number of questions, we can't determine an exact rate; however, we will denote it as \( R_J = \frac{Q}{20} \).
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Ashley’s Rate of Change:
- Ashley makes an average of 21 hot dogs during her 6-hour shift: \[ \text{Rate of change (R)} = \frac{\text{Change in y (hot dogs)}}{\text{Change in x (hours)}} = \frac{21}{6} = 3.5 \]
- Thus, Ashley's rate of change is \( R_A = 3.5 \) hot dogs per hour.
Comparing Rates of Change: To compare the rates, we need a value for \( Q \) in Jamie's case. If, for example, Jamie finished 40 questions in 20 minutes, then: \[ R_J = \frac{40}{20} = 2 \text{ questions per minute} = 120 \text{ questions per hour} \]
If \( Q = 40 \) questions:
- Jamie's rate of change = 120 questions/hour, which is greater than Ashley's 3.5 hot dogs/hour.
- Plotting Ordered Pairs: We can create ordered pairs from both scenarios:
For Jamie (if she finishes 40 questions in 20 minutes):
- If she finishes 120 questions in 60 minutes, we would consider:
- (0, 0), (20, 40), (40, 80), (60, 120)
For Ashley:
- For her average of 21 hot dogs in 6 hours:
- (0, 0), (1, 3.5), (2, 7), (3, 10.5), (4, 14), (5, 17.5), (6, 21)
Since we are plotting only whole-number coordinates, we'll take whole numbers for Jamie:
- Jamie: (0,0), (20,40) (we can scale to whole numbers for hour values if you'd like).
Final coordinates for plotting:
- Jamie: (0, 0), (20, 40)
- Ashley: (0, 0), (6, 21) (but the hour mark may change based on the accuracy expected).
Overall: Assuming Jamie finishes 40 questions as an example, she has a greater rate of change than Ashley. You can graph these ordered pairs on a coordinate plane where the x-axis represents time in minutes/hours and the y-axis represents the number of questions or hot dogs, and you'll observe their respective trends.