8. The tables below show the number of jumping jacks completed after a given period of time in minutes.

Question

Kimberly

Time (min) # Jumping Jacks
3 28
8 58
12 82
16 106
Katrina

Time (min) # Jumping Jacks
2 16
5 40
12 96
20 160


(3 points)
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The person doing the most jumping jacks per minute
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

Answer 1

To answer the questions based on the data provided:

1. The person doing the most jumping jacks per minute: Calculate the rate of jumping jacks per minute for both Kimberly and Katrina.

   • Kimberly (using the last recorded time and number of jumping jacks):

     • 106 jumping jacks at 16 minutes: \[ \text{Rate}_{\text{Kimberly}} = \frac{106}{16} \approx 6.625 , \text{jumping jacks/min} \]

   • Katrina (using the last recorded time and number of jumping jacks):

     • 160 jumping jacks at 20 minutes: \[ \text{Rate}_{\text{Katrina}} = \frac{160}{20} = 8 , \text{jumping jacks/min} \]

   Answer: Katrina

2. The person showing a proportional relationship between time and # of jumping jacks: Check for a constant ratio (the same rate of change).

   • For Kimberly:

     • Rates:
       • 28/3 ≈ 9.33
       • (58-28)/(8-3)=30/5=6
       • (82-58)/(12-8)=24/4=6
       • (106-82)/(16-12)=24/4=6
     • Not consistent.

   • For Katrina:

     • Rates:
       • 16/2 = 8
       • (40-16)/(5-2) = 24/3 = 8
       • (96-40)/(12-5) = 56/7 = 8
       • (160-96)/(20-12) = 64/8 = 8
     • Consistent.

   Answer: Katrina

3. The person that did the most jumping jacks initially before the time started: The first recorded jumping jacks count.

   • Kimberly starts with 28 jumping jacks at 3 minutes.
   • Katrina starts with 16 jumping jacks at 2 minutes.

   Answer: Kimberly

To summarize:

• The person doing the most jumping jacks per minute: Katrina
• The person showing a proportional relationship between time and # of jumping jacks: Katrina
• The person that did the most jumping jacks initially before the time started: Kimberly