To find the score Carlos needs in his last game to average 25 points per game after 7 games, we first need to calculate his total score for the 6 games he has already played. The scores are as follows:
- Game 1: 27 points
- Game 2: 18 points
- Game 3: 24 points
- Game 4: 32 points
- Game 5: 15 points
- Game 6: 27 points
Now, let's sum these scores:
\[ 27 + 18 + 24 + 32 + 15 + 27 = 143 \]
Carlos needs to play one more game, which we'll call \( s \) (the score in the last game). To find \( s \) so that he averages 25 points over 7 games, we can use the equation for average:
\[ \frac{\text{Total points scored}}{\text{Number of games}} = \text{Desired average} \]
This translates to:
\[ \frac{143 + s}{7} = 25 \]
To isolate \( s \), we can multiply both sides of the equation by 7:
\[ 143 + s = 25 \times 7 \]
Calculating \( 25 \times 7 \) gives us:
\[ 143 + s = 175 \]
Now, subtract 143 from both sides to find \( s \):
\[ s = 175 - 143 \] \[ s = 32 \]
So, Carlos needs to score 32 points in his last game to average 25 points per game.
From the options listed in your question, the correct equation that helps find the score \( s \) is:
\[ \frac{27 + 18 + 24 + 32 + 15 + 27 + s}{7} = 25 \]
The equivalent correct version of this from your choices is:
\[ 27 + 18 + 24 + 32 + 15 + 27 + s / 7 = 25, \]
but ensure the parentheses are correctly positioned to reflect the total points divided by 7.