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.