To find the score Carlos needs in the last game to average 25 points per game over 7 games, we can start by calculating the total points he needs to achieve that average.
To achieve an average of 25 points over 7 games, the total points required would be:
\[ 25 \times 7 = 175 \text{ points} \]
Now, let's calculate the total points Carlos has scored in the previous 6 games:
\[ 27 + 18 + 24 + 32 + 15 + 27 = 143 \text{ points} \]
Let \( s \) be the score in the last game. To find how many points he needs in the last game, we can set up the equation:
\[ 143 + s = 175 \]
To solve for \( s \):
\[ s = 175 - 143 \]
\[ s = 32 \]
So, Carlos needs to score 32 points in the last game to achieve an average of 25 points per game.
In terms of the responses given, the correct equation that represents the scenario to find \( s \) (the score for his last game) is:
\[ \frac{27 + 18 + 24 + 32 + 15 + 27 + s}{7} = 25 \]
This can be rewritten as:
\[ 27 + 18 + 24 + 32 + 15 + 27 + s = 25 \cdot 7 \]
Which simplifies to:
\[ 143 + s = 175 \]
So the answer choice you would want is:
\[ \frac{27 + 18 + 24 + 32 + 15 + 27 + s}{7} = 25 \]
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