To find the rate of change of chicken per person in this situation, we need to calculate the amount of chicken cooked per person for each case and then compare the two rates.
For the first case:
- Amount of chicken: 9 lbs
- Number of people: 36
Rate of chicken per person for the first case: \[ \text{Rate}_1 = \frac{9 \text{ lbs}}{36 \text{ people}} = \frac{9}{36} = \frac{1}{4} \text{ lbs/person} \]
For the second case:
- Amount of chicken: 17 lbs
- Number of people: 68
Rate of chicken per person for the second case: \[ \text{Rate}_2 = \frac{17 \text{ lbs}}{68 \text{ people}} = \frac{17}{68} = \frac{1}{4} \text{ lbs/person} \]
Now, both rates of chicken per person are the same: \[ \text{Rate}_1 = \text{Rate}_2 = \frac{1}{4} \text{ lbs/person} \]
Thus, there is no change in the rate of chicken per person between the two situations. The chef consistently cooks \( \frac{1}{4} \) lbs of chicken per person in both cases.
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