Question

Jamal 的抽屉里有 $6$ 只绿色袜子、 $18$ 只紫色袜子和 $12$ 只橙色袜子。加入一些紫色袜子后，Jamal 注意到现在随机抽到一只紫色袜子的概率是 $60\%$ 。Jamal 加入了多少只紫色袜子？

Jamal has a drawer containing $6$ green socks, $18$ purple socks, and $12$ orange socks. After adding more purple socks, Jamal noticed that there is now a $60\%$ chance that a sock randomly selected from the drawer is purple. How many purple socks did Jamal add?

$6$

$9$

$12$

$18$

$24$

答案：B

知识点：基本概率一次方程

难度评级：1020

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文字解答：

设 Jamal 加入 $s$ 只紫色袜子，则紫色袜子共有 $s+18$ 只。

原来共有 $36$ 只袜子，加入后总数为 $s+36$ 只。

因为之后抽到紫色袜子的概率是 $60\%$ ，所以 $\dfrac{s+18}{s+36}=0.6.$

解 $s$ 得 $\begin{align*}s+18 &= 0.6s+21.6 \\ 0.4s &= 3.6\\ s &= 9.\end{align*}$

所以加入了 $9$ 只袜子。

正确答案是 B。

Suppose Jamal adds $s$ purple socks. Then, there will be $s+18$ purple socks.

Also, since there are $36$ total socks to begin with, we have $s+36$ socks after adding the socks.

Since we have a $60\%$ chance of choosing a purple sock afterwards, we know $\dfrac{s+18}{s+36}=0.6.$

Solving for $s$ yields: $\begin{align*}s+18 &= 0.6s+21.6 \\ 0.4s &= 3.6\\ s &= 9.\end{align*}$

Therefore, $9$ socks are added.

Thus, the correct answer is B.

2020 AMC 8 第 13 题

答案：B

难度评级：1020

视频讲解：

文字解答：

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