2013 AMC 12A 第 6 题

Question

在最近的一场篮球比赛中，Shenille 只出手三分球和两分球。她的三分球命中率为

20\%

，两分球命中率为

30\%

。Shenille 一共出手

30

次。她得了多少分？

In a recent basketball game, Shenille attempted only three-point shots and two-point shots. She was successful on

20\%

of her three-point shots and

30\%

of her two-point shots. Shenille attempted

30

shots. How many points did she score?

12

18

24

30

36

设三分球出手次数为

x

，则两分球出手次数为

30 - x

Let

x

be the number of three-point attempts, so

30 - x

are two-point attempts

她的得分为

0.2\cdot 3\cdot x + 0.3\cdot 2\cdot(30 - x)

；其中

x

项会抵消

Her score is

0.2\cdot 3\cdot x + 0.3\cdot 2\cdot(30 - x);

the

x

terms cancel

如果 Shenille 出手

x

次三分球、

30 - x

次两分球，那么她的得分为

\begin{gathered} 0.2\cdot 3\cdot x + 0.3\cdot 2\cdot(30 - x) \\ = 0.6x + 0.6(30 - x) \\ = 0.6\cdot 30 = 18 \end{gathered}

分。

因此，正确答案是 B。

If Shenille attempted

x

three-point shots and

30 - x

two-point shots, she scored

\begin{gathered} 0.2\cdot 3\cdot x + 0.3\cdot 2\cdot(30 - x) \\ = 0.6x + 0.6(30 - x) \\ = 0.6\cdot 30 = 18 \end{gathered}

points.

Thus, the correct answer is B.

其他年份的第 6 题