To find the equation that helps determine the score Carlos needs in the last game to average 25 points over the 7 games, we first calculate the total points he needs to average 25 points per game over 7 games.
The total points needed for an average of 25 points over 7 games is: \[ 25 \times 7 = 175 \]
Next, we can sum the points that Carlos has already scored in the first 6 games: \[ 27 + 18 + 24 + 32 + 15 + 27 \] Calculating this gives: \[ 27 + 18 = 45 \ 45 + 24 = 69 \ 69 + 32 = 101 \ 101 + 15 = 116 \ 116 + 27 = 143 \]
Now, if we let \( s \) represent the points Carlos scores in the last game, he needs to satisfy: \[ 143 + s = 175 \]
Rearranging this gives: \[ s = 175 - 143 \] Thus, \[ s = 32 \]
Now we can write an equation to find \( s \), the score in the last game. The correct equation to represent this is: \[ \frac{27 + 18 + 24 + 32 + 15 + 27 + s}{7} = 25 \]
This translates to: \[ \frac{143 + s}{7} = 25 \]
Comparing that to the provided options, the correct choice is: \[ \frac{27 + 18 + 24 + 32 + 15 + 27 + s}{7} = 25 \] which can be expressed as: \[ \frac{143 + s}{7} = 25 \]
So the option is: \[ 27 + 18 + 24 + 32 + 15 + 27 + s \over 7 = 25 \]
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