2013 AMC 10B 第 10 题

Question

一支篮球队两分球命中率为

50\%

，三分球命中率为

40\%

，共得到

54

分。他们两分球出手次数比三分球多

50\%

。他们出手了多少次三分球？

A basketball team’s players were successful on

50\%

of their two-point shots and

40\%

of their three-point shots, which resulted in

54

points. They attempted

50\%

more two-point shots than three-point shots. How many three-point shots did they attempt?

10

15

20

25

30

答案：C

知识点：百分数一次方程

难度评级：1280

小提示：

设三分球出手次数为

x

。

Let

x

be the number of three-point attempts

大提示：

用

x

表示两类投篮的总得分。

Translate made-shot percentages into total points in terms of

x

解答：

设三分球出手

t

次。

三分球命中

0.4 t

次，得分为

1.2t

。

两分球出手

1.5t

次，命中

0.75t

次，得分为

1.5t

。

因此总分满足

2.7t=54\text{，}

所以

t=20

。

所以正确答案是 C。

Let

t

be the number of three-point attempts.

The number of made three-point shots is

0.4 t,

giving

1.2t

points.

The number of two-point attempts is

1.5t,

so the number made is

0.75t,