Question

在一场 $50$ 题的选择题数学竞赛中，学生每答对一题得 $4$ 分，空题得 $0$ 分，答错一题得 $-1$ 分。Jesse 的总分为 $99$ 。Jesse 最多可能答对多少题？

On a $50$ -question multiple choice math contest, students receive $4$ points for a correct answer, $0$ points for an answer left blank, and $-1$ point for an incorrect answer. Jesse’s total score on the contest was $99.$ What is the maximum number of questions that Jesse could have answered correctly?

$25$

$27$

$29$

$31$

$33$

答案：C

知识点：一次方程不等式最优化

难度评级：1420

解答：

设 Jesse 答对 $x$ 题，答错 $y$ 题。

因此必须同时满足 $4x - y = 99 \text{ and } x + y \leq 50.$

由代入得到 $y = 4x - 99$ $5x - 99 \leq 50.$

因为 $x$ 是整数，而 $x \leq 29.8$ ，所以最大值为 $29$ 。

所以正确答案是 C。

Let $x$ be the number of questions Jesse answered correctly and $y$ be the number he answered incorrectly.

Then $4x - y = 99 \text{ and } x + y \leq 50.$

We have that $y = 4x - 99$ $5x - 99 \leq 50.$

Rearranging and simplifying tells us that $x \leq 29.8.$ Since $x$ is an integer, its maximum value is $29.$

Thus, C is the correct answer.

2010 AMC 10B 第 15 题

答案：C

难度评级：1420

解答：

其他年份的第 15 题