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Answer :
To determine the minimum number of teams needed for a recreational softball league with 118 players, where each team can have a maximum of 14 players, we need to use an inequality.
1. Understand the Problem:
- Total players: 118
- Maximum players per team: 14
2. Set Up the Inequality:
- We want to assign all 118 players to teams, and each team can have at most 14 players. This means the number of teams, [tex]\( t \)[/tex], should be sufficient to cover all 118 players.
- The inequality representing this situation is [tex]\( 14t \geq 118 \)[/tex]. This inequality ensures that the total capacity of all teams combined (i.e., [tex]\( 14 \times t \)[/tex]) is at least 118.
3. Solution to the Inequality:
- Solving [tex]\( 14t \geq 118 \)[/tex] for [tex]\( t \)[/tex], we need to find the smallest integer [tex]\( t \)[/tex] that satisfies this inequality.
- Dividing both sides of the inequality by 14 gives [tex]\( t \geq \frac{118}{14} \)[/tex].
4. Calculate:
- Compute [tex]\( \frac{118}{14} \approx 8.4286 \)[/tex].
- Since [tex]\( t \)[/tex] must be a whole number (you can’t have a fraction of a team), we round up to the nearest whole number, meaning [tex]\( t \)[/tex] has to be at least 9.
Therefore, the minimum number of teams needed is 9, which aligns with the inequality [tex]\( 14t \geq 118 \)[/tex]. The correct answer is option C.
1. Understand the Problem:
- Total players: 118
- Maximum players per team: 14
2. Set Up the Inequality:
- We want to assign all 118 players to teams, and each team can have at most 14 players. This means the number of teams, [tex]\( t \)[/tex], should be sufficient to cover all 118 players.
- The inequality representing this situation is [tex]\( 14t \geq 118 \)[/tex]. This inequality ensures that the total capacity of all teams combined (i.e., [tex]\( 14 \times t \)[/tex]) is at least 118.
3. Solution to the Inequality:
- Solving [tex]\( 14t \geq 118 \)[/tex] for [tex]\( t \)[/tex], we need to find the smallest integer [tex]\( t \)[/tex] that satisfies this inequality.
- Dividing both sides of the inequality by 14 gives [tex]\( t \geq \frac{118}{14} \)[/tex].
4. Calculate:
- Compute [tex]\( \frac{118}{14} \approx 8.4286 \)[/tex].
- Since [tex]\( t \)[/tex] must be a whole number (you can’t have a fraction of a team), we round up to the nearest whole number, meaning [tex]\( t \)[/tex] has to be at least 9.
Therefore, the minimum number of teams needed is 9, which aligns with the inequality [tex]\( 14t \geq 118 \)[/tex]. The correct answer is option C.
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