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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.
Write an inequality that represents the number of games Fabiano should win
(W) and draw
(D) to achieve his goal.

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. $\newline$ Write an inequality that represents the number of games Fabiano should win $\newline$ $(W)$ and draw $\newline$ $(D)$ to achieve his goal.

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Modeling with linear inequalities

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.

\newline

Write an inequality that represents the number of games Fabiano should win

\newline

(W)

and draw

\newline

(D)

to achieve his goal.

Set Up Equation: Fabiano scores $1$ point for each win and $0.5$ points for each draw. To find the inequality that represents the number of games he should win $(W)$ and draw $(D)$ to achieve at least $6.5$ points, we can set up an equation where the total points from wins and draws are equal to or greater than $6.5$ .
Assign Points: Let's assign the value of $1$ point to each win ( $W$ ) and $0.5$ points to each draw ( $D$ ). The inequality will then be the sum of points from wins and draws being greater than or equal to $6.5$ . So, the inequality is: $1\times W + 0.5\times D \geq 6.5$ .
Check Inequality: We need to check if the inequality makes sense. If Fabiano wins $0$ games and draws $0$ games, he would score $0$ points, which is less than $6.5$ . If he wins $7$ games and draws $0$ games, he would score $7$ points, which is more than $6.5$ . This means the inequality is set up correctly.

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