2013 AMC 10A 第 9 题

Question

在最近一场篮球比赛中，Shenille 只投三分球和两分球。她三分球命中率为

20\%

，两分球命中率为

30\%

。Shenille 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

设两分球和三分球出手数分别为

x

和

y

。

Let

x

and

y

be the numbers of two-point and three-point attempts

计算每种出手平均贡献多少分。

Compare the points earned per attempted shot type after applying the success percentages

设两分球出手

x

次，三分球出手

y

次。

那么 Shenille 命中

0.3x

个两分球和

0.2y

个三分球，总得分为

2 \cdot 0.3x + 3 \cdot 0.2y = 0.6x + 0.6y\text{。}

我们知道

x + y = 30

0.6(x + y) = 18\text{。}

所以正确答案是 B。

Let

x

be the number of two-point shots and

y

be the number of three-point shots.

Then, Shenille makes

0.3x

two-point shots and

0.2y

three-point shots, for a total score of

2 \cdot 0.3x + 3 \cdot 0.2y = 0.6x + 0.6y.

We know that

x + y = 30

0.6(x + y) = 18.

Thus, B is the correct answer.

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