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The average goal scored by 15 selected players in EPL is 16. The maximum number of goals scored by a player is 20 and the minimum is 12. The goals scored by players are between 12 and 20. What can be the maximum number of players who scored at least 18 goals?
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The average goal scored by 15 selected players in EPL is 16. The maxim...
To determine the maximum number of players who scored at least 18 goals among the 15 selected players in the EPL, we need to analyze the given data carefully.

Understanding the Average Goals
- The average goals scored by the 15 players is 16.
- Therefore, the total goals scored by all players = 15 players × 16 goals = 240 goals.

Setting the Constraints
- The maximum goals scored by a player = 20.
- The minimum goals scored by a player = 12.
- Goals scored by players range from 12 to 20.

Calculating Maximum Players with 18+ Goals
1. **Assume 'x' players scored at least 18 goals**:
- Let’s denote these players as scoring either 18, 19, or 20 goals.
- If 'x' players scored 18 goals, their contribution would be 18x.
2. **Rest of the Players**:
- The remaining (15 - x) players must score between 12 and 16 goals to keep the average at 16.
- To minimize their total, assume they all score 12 goals:
- Contribution = 12(15 - x).
3. **Setting Up the Equation**:
- Total goals equation: 240 = 18x + 12(15 - x).
- Simplifying gives: 240 = 18x + 180 - 12x.
- Thus, 240 = 6x + 180.
- This leads to: 6x = 60 → x = 10.

Conclusion
- Hence, the maximum number of players who scored at least 18 goals is **10**.
- The remaining 5 players can score 12 goals each, maintaining the average at 16 while allowing for 10 players to meet the 18-goal threshold.
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The average goal scored by 15 selected players in EPL is 16. The maximum number of goals scored by a player is 20 and the minimum is 12. The goals scored by players are between 12 and 20. What can be the maximum number of players who scored at least 18 goals?
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