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?

$12$

$18$

$24$

$30$

$36$

答案：B

知识点：百分数不变量

难度评级：1250

小提示：

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

大提示：

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

解答：

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.

2013 AMC 12A 第 6 题

答案：B

难度评级：1250

小提示：

大提示：

解答：

其他年份的第 6 题