Question

in a beanbag toss game, janelle scores 5 points for landing on a round target and 8 points for landing on a square target. she needs more than 50 points to win. let \\(x\\) represent the number of times janelle lands on the round target and let \\(y\\) represent the number of times she lands on the square target. which inequality represents the situation?

\\(5x + 8y > 50\\)
\\(5x + 8y \ge 50\\)
\\(8x + 5y > 50\\)
\\(8x + 5y < 50\\)

Explanation:

Identify the variables and coefficients

Using the Real-world Constraints knowledge point

• Round target score: \(5\) points per land.
• Square target score: \(8\) points per land.
• Let \(x\) be round target lands.
• Let \(y\) be square target lands.

Formulate the total score expression

Using the Linear Inequalities knowledge point

$$ \text{Total Score} = 5x + 8y $$

Determine the inequality sign

Using the Linear Inequalities knowledge point

• Target score needed: more than \(50\) points.
• "More than" corresponds to \(>\).

$$ 5x + 8y > 50 $$

Answer:

• (A) \(5x + 8y > 50\) (Correct answer)
• (B) \(5x + 8y \ge 50\)
• (C) \(8x + 5y > 50\)
• (D) \(8x + 5y < 50\)