To find the score Carlos needs in the last game to achieve an average of 25 points per game over 7 games, we start by establishing the equation for the average score.
First, we calculate the total points he needs to average 25 points over 7 games:
\[ \text{Total points needed} = 25 \text{ points/game} \times 7 \text{ games} = 175 \text{ points} \]
Next, we calculate the total points he has scored in the first 6 games:
\[ 27 + 18 + 24 + 32 + 15 + 27 = 143 \text{ points} \]
Let \( s \) be the score in the last game. The equation can be set up as follows:
\[ 143 + s = 175 \]
To find \( s \), we rearrange the equation:
\[ s = 175 - 143 \] \[ s = 32 \]
Now, let's reflect on the multiple choice responses you provided:
- \( \frac{143s}{7} = 25 \) (this does not represent the average correctly)
- \( \frac{27 + 18 + 24 + 32 + 15 + 17 + s}{7} = 25 \) (incorrect, it includes a mistake with the scores)
- \( \frac{27 + 18 + 24 + 32 + 15 + 27 + s}{7} = 25 \) (this matches, except it has a typo in the scores, representing the scores incorrectly)
- \( \frac{27 + 18 + 24 + 32 + 15 + 277 + s}{25} \) (this is not correct)
Therefore, the best fitting equation you can use to determine Carlos' score for his last game to average 25 points across 7 games is:
\[ \frac{143 + s}{7} = 25 \]
Even though none of the options listed perfectly reflect this, you can use the derived equation to find the score Carlos needs in his last game.
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