To find the score Carlos needs in the last game to achieve an average of 25 points per game over 7 games, we first calculate the total number of points he needs.
If Carlos wants to average 25 points over 7 games, he will need a total of: \[ 25 \times 7 = 175 \text{ points} \]
Next, let's calculate the total points he has scored in his first 6 games: \[ 27 + 18 + 24 + 32 + 15 + 27 = 143 \text{ points} \]
Let \( s \) represent the points scored in the last game. To find the score Carlos needs in the last game, we can set up the following equation:
\[ 143 + s = 175 \]
From this equation, we can determine \( s \): \[ s = 175 - 143 = 32 \]
Thus, the score Carlos needs in the last game to achieve an average of 25 points is 32.
Among the provided options, the correct equation would be the one that represents the requirement to reach the total needed points for an average. The correct format includes the sum of all his points over the number of games:
\[ \frac{143 + s}{7} = 25 \] This would imply the proper equation that means Carlos needs to average 25 points per game.
However, unfortunately, none of the provided options are formatted correctly. The best representation would be:
\[
\frac{143 + s}{7} = 25
\]
But this is not listed in your options. If you are required to choose, compute based on which option is closest in logic. The first response comes closest to the average calculation. Hence use:
\[
Start Fraction 143 + s over 7 End Fraction equals 25
\]
If you want clarity, use the first option with the correct formula.