To find the score Carlos needs in the last game to average 25 points per game over 7 games, we need to first sum his scores from the previous 6 games and add the score from the last game (let's denote it as \( s \)). Then we will divide that sum by 7 (the total number of games) and set it equal to 25.
The total points scored in the first 6 games is:
\[ 27 + 18 + 24 + 32 + 15 + 27 = 143 \]
Now we want to form the equation based on the average:
\[ \frac{143 + s}{7} = 25 \]
This means that the correct choice among the provided options should reflect this equation.
- Option A and C do not include the correct sum (either using the wrong numbers or have the wrong structure).
- Option D is missing a mathematical operator and doesn't convey the intended equality correctly.
The correct choice based on the sum and average above should be formatted as:
\[ \frac{143 + s}{7} = 25 \]
But since this wasn't listed among the options, the best and closest representation is Option B:
B: \(\frac{27 + 18 + 24 + 32 + 15 + 27 + s}{7} = 25\)
This option correctly represents the sum of the first six games and includes \( s \), indicating the score in the last game. Although it is mathematically equivalent, it's structured correctly to communicate the calculation needed.