Question

一个篮球队的队员投进了一些三分球、一些两分球和一些一分罚球。他们由两分球得到的分数与由三分球得到的分数一样多。他们罚中的次数比投中的两分球次数多一。球队总得分为 $61$ 分。他们罚中了多少球？

The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team’s total score was $61$ points. How many free throws did they make?

$13$

$14$

$15$

$16$

$17$

答案：A

知识点：方程组换元法

难度评级：1170

小提示：

设投中的两分球个数为 $a$ ；两分球和三分球得到的分数各为 $2a$

Let $a$ be the number of two-point shots; the points from two-point and three-point shots are each $2a$

大提示：

罚球个数为 $a + 1$ ，所以总分为 $2a + 2a + (a + 1)$

The free throws number $a + 1,$ so the total is $2a + 2a + (a + 1)$

解答：

设投中的两分球个数为 $a$ 。两分球得到 $2a$ 分，三分球也得到同样的 $2a$ 分。罚球个数为 $a + 1$ ，得到 $a + 1$ 分。

总分为 $\begin{aligned} 2a + 2a + (a + 1) \\ = 5a + 1 = 61 \end{aligned}\text{，}$ 所以 $a = 12$ ，罚球个数为 $a + 1 = 13$ 。

因此，正确答案是 A。

Let $a$ be the number of two-point shots. The two-point shots score $2a$ points, and the three-point shots score the same $2a$ points. The free throws number $a + 1$ and score $a + 1$ points.

The total is $\begin{aligned} 2a + 2a + (a + 1) \\ = 5a + 1 = 61, \end{aligned}$ so $a = 12$ and the free throws number $a + 1 = 13.$

Thus, the correct answer is A.

2011 AMC 12A 第 6 题

答案：A

难度评级：1170

小提示：

大提示：

解答：

其他年份的第 6 题