Question
The tables below shows the number of jumping jacks completed after a given period of time in minutes.
Kimberly
Time (min) | 3 | 8 | 12 | 16
# Jumping Jacks | 28 | 58 | 82 | 106
Katrina
Time (min) | 2 | 5 | 12 | 20
# Jumping Jacks | 16 | 40 | 96 | 160
The person showing a proportional relationship between time and # of jumping jacks ___________
The person that did the most jumping jacks initially before the time started _____________
The person doing the most jumping jacks per minute _______________
Options: Katrina, Kimberly, Neither, Both
Kimberly
Time (min) | 3 | 8 | 12 | 16
# Jumping Jacks | 28 | 58 | 82 | 106
Katrina
Time (min) | 2 | 5 | 12 | 20
# Jumping Jacks | 16 | 40 | 96 | 160
The person showing a proportional relationship between time and # of jumping jacks ___________
The person that did the most jumping jacks initially before the time started _____________
The person doing the most jumping jacks per minute _______________
Options: Katrina, Kimberly, Neither, Both
Answers
GPT-4o mini
Let's analyze the data for Kimberly and Katrina to answer the questions.
### For Kimberly:
- At 3 minutes: 28 jumping jacks
- At 8 minutes: 58 jumping jacks
- At 12 minutes: 82 jumping jacks
- At 16 minutes: 106 jumping jacks
To check the proportionality, we can examine the number of jumping jacks per minute:
- From 3 to 8 minutes: (58 - 28) / (8 - 3) = 30 / 5 = 6 jumping jacks per minute
- From 8 to 12 minutes: (82 - 58) / (12 - 8) = 24 / 4 = 6 jumping jacks per minute
- From 12 to 16 minutes: (106 - 82) / (16 - 12) = 24 / 4 = 6 jumping jacks per minute
Kimberly shows a consistent rate of 6 jumping jacks per minute after the first data point.
### For Katrina:
- At 2 minutes: 16 jumping jacks
- At 5 minutes: 40 jumping jacks
- At 12 minutes: 96 jumping jacks
- At 20 minutes: 160 jumping jacks
Checking the number of jumping jacks per minute:
- From 2 to 5 minutes: (40 - 16) / (5 - 2) = 24 / 3 = 8 jumping jacks per minute
- From 5 to 12 minutes: (96 - 40) / (12 - 5) = 56 / 7 = 8 jumping jacks per minute
- From 12 to 20 minutes: (160 - 96) / (20 - 12) = 64 / 8 = 8 jumping jacks per minute
Katrina also shows a consistent rate of 8 jumping jacks per minute.
### Summary of Analysis:
1. **Proportional relationship**:
- Both Kimberly and Katrina have a consistent rate of jumping jacks per minute.
- Therefore, the answer is **Both**.
2. **Most jumping jacks initially before time started**:
- Kimberly has 28 jumping jacks at 3 minutes, while Katrina has 16 jumping jacks at 2 minutes.
- Therefore, the answer is **Kimberly**.
3. **Most jumping jacks per minute**:
- Kimberly: 6 jumping jacks per minute
- Katrina: 8 jumping jacks per minute
- Therefore, the answer is **Katrina**.
### Final Answers:
1. The person showing a proportional relationship between time and # of jumping jacks: **Both**
2. The person that did the most jumping jacks initially before the time started: **Kimberly**
3. The person doing the most jumping jacks per minute: **Katrina**
### For Kimberly:
- At 3 minutes: 28 jumping jacks
- At 8 minutes: 58 jumping jacks
- At 12 minutes: 82 jumping jacks
- At 16 minutes: 106 jumping jacks
To check the proportionality, we can examine the number of jumping jacks per minute:
- From 3 to 8 minutes: (58 - 28) / (8 - 3) = 30 / 5 = 6 jumping jacks per minute
- From 8 to 12 minutes: (82 - 58) / (12 - 8) = 24 / 4 = 6 jumping jacks per minute
- From 12 to 16 minutes: (106 - 82) / (16 - 12) = 24 / 4 = 6 jumping jacks per minute
Kimberly shows a consistent rate of 6 jumping jacks per minute after the first data point.
### For Katrina:
- At 2 minutes: 16 jumping jacks
- At 5 minutes: 40 jumping jacks
- At 12 minutes: 96 jumping jacks
- At 20 minutes: 160 jumping jacks
Checking the number of jumping jacks per minute:
- From 2 to 5 minutes: (40 - 16) / (5 - 2) = 24 / 3 = 8 jumping jacks per minute
- From 5 to 12 minutes: (96 - 40) / (12 - 5) = 56 / 7 = 8 jumping jacks per minute
- From 12 to 20 minutes: (160 - 96) / (20 - 12) = 64 / 8 = 8 jumping jacks per minute
Katrina also shows a consistent rate of 8 jumping jacks per minute.
### Summary of Analysis:
1. **Proportional relationship**:
- Both Kimberly and Katrina have a consistent rate of jumping jacks per minute.
- Therefore, the answer is **Both**.
2. **Most jumping jacks initially before time started**:
- Kimberly has 28 jumping jacks at 3 minutes, while Katrina has 16 jumping jacks at 2 minutes.
- Therefore, the answer is **Kimberly**.
3. **Most jumping jacks per minute**:
- Kimberly: 6 jumping jacks per minute
- Katrina: 8 jumping jacks per minute
- Therefore, the answer is **Katrina**.
### Final Answers:
1. The person showing a proportional relationship between time and # of jumping jacks: **Both**
2. The person that did the most jumping jacks initially before the time started: **Kimberly**
3. The person doing the most jumping jacks per minute: **Katrina**