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Fabiano wants to score at least 6.56.5 points in a major chess tournament. He scores 11 point for each game that he wins, and he scores 0.50.5 points for each game that ends in a draw. Which of the following inequalities represents the number of games Fabiano should win (W)(W) and draw (D)(D) to achieve his goal?\newlineChoose 11 answer:\newline(A) W+0.5D≤6.5W+0.5D \leq 6.5\newline(B) 0.5W+D≥6.50.5W+D \geq 6.5\newline(C) W+0.5D≥6.5W+0.5D \geq 6.5\newline(D) 0.5W+D≤6.50.5W+D \leq 6.5

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Q. Fabiano wants to score at least 6.56.5 points in a major chess tournament. He scores 11 point for each game that he wins, and he scores 0.50.5 points for each game that ends in a draw. Which of the following inequalities represents the number of games Fabiano should win (W)(W) and draw (D)(D) to achieve his goal?\newlineChoose 11 answer:\newline(A) W+0.5D≤6.5W+0.5D \leq 6.5\newline(B) 0.5W+D≥6.50.5W+D \geq 6.5\newline(C) W+0.5D≥6.5W+0.5D \geq 6.5\newline(D) 0.5W+D≤6.50.5W+D \leq 6.5
  1. Scoring System: Fabiano scores 11 point for each win (WW) and 0.50.5 points for each draw (DD). To achieve at least 6.56.5 points, the total points from wins and draws should be equal to or greater than 6.56.5.
  2. Translate into Inequality: Translate the scoring system into an inequality. Each win is 11 point, so it contributes WW points. Each draw is 0.50.5 points, so it contributes 0.5D0.5D points. The sum of these should be at least 6.56.5 points.
  3. Write the Inequality: Write the inequality based on the previous step: W+0.5D≥6.5W + 0.5D \geq 6.5.
  4. Check the Options: Check the options given to see which one matches the inequality we have derived.\newline(A) W+0.5D≤6.5W + 0.5D \leq 6.5 (This suggests Fabiano should score at most 6.56.5 points, which is incorrect.)\newline(B) 0.5W+D≥6.50.5W + D \geq 6.5 (This does not correctly represent the scoring system.)\newline(C) W+0.5D≥6.5W + 0.5D \geq 6.5 (This matches our inequality and correctly represents the condition for Fabiano's goal.)\newline(D) 0.5W+D≤6.50.5W + D \leq 6.5 (This also does not correctly represent the scoring system and suggests scoring at most 6.56.5 points.)
  5. Identify the Correct Answer: Identify the correct answer based on the inequality we have written: W+0.5D≥6.5W + 0.5D \geq 6.5, which corresponds to option (C).

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