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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

1 answer

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