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Fabiano wants to score at least 6.5 points in a major chess tournament. He scores 1 point for each game that he wins, and he scores 0.5 points for each game that ends in a draw. Which of the following inequalities represents the number of games Fabiano should win
(W) and draw
(D) to achieve his goal?
Choose 1 answer:
(A)
W+0.5 D <= 6.5
(B)
0.5 W+D >= 6.5
(c)
W+0.5 D >= 6.5
(D)
0.5 W+D <= 6.5

Fabiano wants to score at least $6$ . $5$ points in a major chess tournament. He scores $1$ point for each game that he wins, and he scores $0$ . $5$ points for each game that ends in a draw. Which of the following inequalities represents the number of games Fabiano should win $(W)$ and draw $(D)$ to achieve his goal? $\newline$ Choose $1$ answer: $\newline$ (A) $W+0.5 D \leq 6.5$ $\newline$ (B) $0.5 W+D \geq 6.5$ $\newline$ (C) $W+0.5 D \geq 6.5$ $\newline$ (D) $0.5 W+D \leq 6.5$

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Counting principle

Full solution

Q. Fabiano wants to score at least

6

.

5

points in a major chess tournament. He scores

1

point for each game that he wins, and he scores

0

.

5

points for each game that ends in a draw. Which of the following inequalities represents the number of games Fabiano should win

(W)

and draw

(D)

to achieve his goal?

\newline

Choose

1

answer:

\newline

(A)

W+0.5 D \leq 6.5

\newline

(B)

0.5 W+D \geq 6.5

\newline

(C)

W+0.5 D \geq 6.5

\newline

(D)

0.5 W+D \leq 6.5

Identify Points Earned: Identify the points Fabiano earns for each win and draw. $\newline$ Fabiano earns $1$ point for each win and $0.5$ points for each draw.
Translate into Equation: Translate the point system into an equation. $\newline$ The total points Fabiano earns can be represented by the equation: Total Points = $1 \times W + 0.5 \times D$ .
Determine Goal Inequality: Determine the inequality that represents Fabiano's goal. $\newline$ Fabiano wants to score at least $6.5$ points, which means the total points should be greater than or equal to $6.5$ . Therefore, the inequality should reflect this goal.
Write Goal Inequality: Write the inequality based on the equation and the goal. $\newline$ The inequality that represents Fabiano's goal is: $1 \times W + 0.5 \times D \geq 6.5$ .
Match Correct Inequality: Match the correct inequality with the given options. $\newline$ The correct inequality is (C) $W + 0.5 D \geq 6.5$ , which matches the inequality we derived.

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