To find the score Carlos needs in his last game to achieve an average of 25 points per game, we can set up an equation based on the total points scored.
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Calculate the total points needed for 7 games: Since he wants to average 25 points per game over 7 games, the total points needed is: \[ \text{Total points needed} = 25 \text{ points/game} \times 7 \text{ games} = 175 \text{ points} \]
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Sum the points scored in the first 6 games: Carlos has scored 27, 18, 24, 32, 15, and 27 points in the first 6 games. Let's sum these points: \[ 27 + 18 + 24 + 32 + 15 + 27 = 143 \text{ points} \]
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Let \( x \) be the score in the last game: To find \( x \), the score needed in the last game, we can set up the equation: \[ \text{Total points scored} = \text{Points from first 6 games} + x \] Therefore, the equation becomes: \[ 143 + x = 175 \]
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Solve for \( x \): \[ x = 175 - 143 \] \[ x = 32 \]
Carlos needs to score 32 points in his last game to achieve an average of 25 points per game.