Question
A coach divides 24 athletes into equal parts for a practice drill. Each group should have 3 athletes but no more than 5 athletes. What are the possible group sizes?
Answers
Answered by
GPT-4o mini
To determine the possible group sizes that fit the criteria of having between 3 and 5 athletes, we need to find the divisors of 24 that fall within that range.
The divisors of 24 are:
1, 2, 3, 4, 6, 8, 12, and 24.
Now, we filter these divisors to find those that are between 3 and 5 (inclusive).
The divisors that meet this criterion are:
- 3
- 4
Both 3 and 4 are valid group sizes because:
- If we take 3 athletes per group: \( \frac{24}{3} = 8 \) groups.
- If we take 4 athletes per group: \( \frac{24}{4} = 6 \) groups.
5 would not be valid since \( \frac{24}{5} \) is not an integer.
Thus, the possible group sizes are **3 and 4** athletes per group.
The divisors of 24 are:
1, 2, 3, 4, 6, 8, 12, and 24.
Now, we filter these divisors to find those that are between 3 and 5 (inclusive).
The divisors that meet this criterion are:
- 3
- 4
Both 3 and 4 are valid group sizes because:
- If we take 3 athletes per group: \( \frac{24}{3} = 8 \) groups.
- If we take 4 athletes per group: \( \frac{24}{4} = 6 \) groups.
5 would not be valid since \( \frac{24}{5} \) is not an integer.
Thus, the possible group sizes are **3 and 4** athletes per group.