To find the score Carlos needs in his last game to achieve an average of 25 points per game, we can set up an equation based on the definition of average.
First, let's denote the score Carlos needs in the last game as \( x \).
Carlos has played 6 games and scored the following points:
- 27
- 18
- 24
- 32
- 15
- 27
Now, let's calculate the total points he has scored in the first 6 games:
\[ 27 + 18 + 24 + 32 + 15 + 27 = 143 \]
Now, Carlos wants his average for all 7 games to be 25 points. The average is found by dividing the total points scored by the number of games. Since he will have played 7 games after the last one, we can write the equation for the average:
\[ \text{Average} = \frac{\text{Total Points}}{\text{Number of Games}} = 25 \]
So we can set up the equation as follows:
\[ \frac{143 + x}{7} = 25 \]
Now, we can solve for \( x \) (the score he needs in the last game):
- Multiply both sides by 7:
\[ 143 + x = 25 \times 7 \]
- Calculate \( 25 \times 7 = 175 \):
\[ 143 + x = 175 \]
- Subtract 143 from both sides:
\[ x = 175 - 143 \]
- Calculate \( 175 - 143 = 32 \):
\[ x = 32 \]
Therefore, Carlos needs to score 32 points in his last game to achieve an average of 25 points per game.
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