1. **Problem Statement:** A family needs at least 350 points to win the Thanksgiving game night prize. Each board game played gives 60 points, and each card game gives 25 points. They can play a maximum of 8 games total. We define: - $B$ = number of board games - $C$ = number of card games We want to find the inequality that represents the condition to win the prize. 2. **Understanding the problem:** - The total points earned from board games is $60B$. - The total points earned from card games is $25C$. - The total points must be at least 350 to win, so the inequality for points is: $$60B + 25C \geq 350$$ - The total number of games played is $B + C$, and since they only have time for a maximum of 8 games, we have: $$B + C \leq 8$$ 3. **Analyzing the answer choices:** - a) $B + C \leq 350$ — This incorrectly compares the number of games to points, so it is not correct. - b) $60B + 25C \leq 350$ — This says total points are less than or equal to 350, which contradicts the "at least 350" requirement. - c) $60B + 25C \geq 8$ — This is a very low threshold and does not represent the prize condition. - d) $60B + 25C \geq 350$ — This correctly represents the minimum points needed to win. 4. **Final answer:** The inequality that represents the situation if they want to win the prize is: $$60B + 25C \geq 350$$ This corresponds to option d. **Note:** The maximum number of games constraint $B + C \leq 8$ is also important but not asked for in the inequality options.