Question

$2007$ 年 AMC $10$ 的计分规则为：每答对一题得 $6$ 分，每答错一题得 $0$ 分，每道未答题得 $1.5$ 分。Sarah 看完 $25$ 道题后决定尝试前 $22$ 题，只留下最后 $3$ 题不答。为了至少得到 $100$ 分，她前 $22$ 题中至少要答对多少题？

The $2007$ AMC $10$ will be scored by awarding $6$ points for each correct response, $0$ points for each incorrect response, and $1.5$ points for each problem left unanswered. After looking over the $25$ problems, Sarah has decided to attempt the first $22$ and leave only the last $3$ unanswered. How many of the first $22$ problems must she solve correctly in order to score at least $100$ points?

$13$

$14$

$15$

$16$

$17$

答案：D

知识点：不等式一次方程

难度评级：1120

小提示：

未答题也会贡献分数。

The unanswered problems still contribute points

大提示：

先减去 $3$ 道空题的分数，再用剩下需要的分数除以 $6$ 。

Subtract the points from the $3$ blanks, then divide the remaining needed points by $6$

解答：

三道空题给 $3\cdot 1.5 = 4.5$ 分，所以 Sarah 需要从前 $22$ 题得到 $100-4.5=95.5$ 分。

因为 $\frac{95.5}{6}$ 介于 $15$ 和 $16$ 之间，她至少要答对 $16$ 题，此时总分为 $100.5$ 。

所以正确答案是 D。

The three blank problems give $3\cdot 1.5 = 4.5$ points, so Sarah needs $100-4.5=95.5$ points from the first $22.$

Since $\frac{95.5}{6}$ lies between $15$ and $16,$ she must answer at least $16$ correctly, which would give a score of $100.5.$

Thus, the correct answer is D.

2007 AMC 10B 第 6 题

答案：D

难度评级：1120

小提示：

大提示：

解答：

其他年份的第 6 题