2011 AMC 12A 第 6 题

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：

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