To find the score Carlos needs in the last game to average 25 points over 7 games, you can start by setting up the equation for the average.
Let \( x \) represent the score Carlos needs in the last game.
First, calculate the total points he has scored in the first 6 games:
\[ 27 + 18 + 24 + 32 + 15 + 27 = 143 \]
Next, since he wants to average 25 points over 7 games, we can set up the following equation for the average:
\[ \text{Average} = \frac{\text{Total Points}}{\text{Number of Games}} \]
For Carlos, this becomes:
\[ 25 = \frac{143 + x}{7} \]
To eliminate the fraction, multiply both sides by 7:
\[ 175 = 143 + x \]
Now, solve for \( x \):
\[ x = 175 - 143 \] \[ x = 32 \]
So, the equation that helps find the score for the last game is:
\[ 175 = 143 + x \]
And Carlos needs to score 32 points in the last game to achieve his goal of averaging 25 points per game.