To determine which club accepts more members each week, we should find the membership growth of the ballet club from the provided table values.
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Chess Club:
- The chess club has 5 new members each week.
- After 6 weeks, it has 37 members.
- The founding members (M_0) can be calculated as: \[ M_0 + 5 \times 6 = 37 \quad \Rightarrow \quad M_0 + 30 = 37 \quad \Rightarrow \quad M_0 = 37 - 30 = 7 \]
- Thus, the chess club had 7 founding members.
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Ballet Club:
- We need to find the number of members at various weeks and determine the rates.
- At week 3: 28 members
- At week 10: 70 members
- At week 17: 112 members
- We can find the number of new members accepted each week by calculating the increase in membership.
From week 3 to week 10: \[ 70 - 28 = 42 \quad \text{members over } (10 - 3) = 7 \text{ weeks} \] \[ \text{Rate for this period} = \frac{42}{7} = 6 \quad \text{members per week} \]
From week 10 to week 17: \[ 112 - 70 = 42 \quad \text{members over } (17 - 10) = 7 \text{ weeks} \] \[ \text{Rate for this period} = \frac{42}{7} = 6 \quad \text{members per week} \]
It appears that members are accepted at a constant rate of 6 members per week.
- We need to find the number of members at various weeks and determine the rates.
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Comparing both clubs:
- Chess club: 5 members per week
- Ballet club: 6 members per week
Conclusion:
- Which club accepts more members each week?
(Choice B) The ballet club
Next, we can determine which club had more founding members:
- Chess club founding members: 7
- Ballet club founding members need to be calculated using the first point in the table (week 3): \[ M_0 + 6 \times 3 = 28 \quad \Rightarrow \quad M_0 + 18 = 28 \quad \Rightarrow \quad M_0 = 28 - 18 = 10 \]
- Therefore, the ballet club had 10 founding members.
Conclusion:
- Which club had more founding members?
(Choice B) The ballet club