To find the score Carlos needs in his last game to achieve an average of 25 points per game, we can set up the following equation.
First, we know that the average is calculated by taking the total points scored and dividing it by the number of games played. Carlos has played 6 games, and we need to find out how many points he should score in the 7th game.
Let's denote the score in the last game as \( x \).
The total points scored over the 6 games can be calculated as follows:
\[ 27 + 18 + 24 + 32 + 15 + 27 = 143 \]
Now, if he scores \( x \) points in the 7th game, the total points after 7 games will be:
\[ 143 + x \]
The average score he wants after 7 games is 25 points. Since he will have played 7 games, we can express this as:
\[ \frac{143 + x}{7} = 25 \]
Now, we can solve this equation for \( x \). First, we multiply both sides by 7:
\[ 143 + x = 175 \]
Now, isolate \( x \) by subtracting 143 from both sides:
\[ x = 175 - 143 \]
\[ x = 32 \]
So, Carlos needs to score 32 points in his last game to achieve an average of 25 points per game.