AMC8 2020

AMC8 2020 · Q13

AMC8 2020 · Q13. It mainly tests Linear equations, Probability (basic).

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?

Jamal 的抽屉里有 6 双绿色袜子、18 双紫色袜子和 12 双橙色袜子。添加更多紫色袜子后，Jamal 注意到现在随机抽取一只袜子是紫色的概率为 60%。Jamal 添加了多少紫色袜子？

(A) 6 6

(B) 9 9

(D) 18 18

(E) 24 24

Answer

Correct choice: (B)

正确答案：（B）

Solution

After Jamal adds $x$ purple socks, he has $(18+x)$ purple socks and $6+18+12+x=(36+x)$ total socks. This means the probability of drawing a purple sock is $\frac{18+x}{36+x}$, so we obtain \[\frac{18+x}{36+x}=\frac{3}{5}\] Since $\frac{18+9}{36+9}=\frac{27}{45}=\frac{3}{5}$, the answer is $\boxed{\textbf{(B) }9}$.

Jamal 添加 $x$ 双紫色袜子后，他有 $(18+x)$ 双紫色袜子，总共 $6+18+12+x=(36+x)$ 双袜子。这意味着抽到紫色袜子的概率是 $\frac{18+x}{36+x}$，所以我们得到 \[\frac{18+x}{36+x}=\frac{3}{5}\] 因为 $\frac{18+9}{36+9}=\frac{27}{45}=\frac{3}{5}$，答案是 $\boxed{\textbf{(B) }9}$。

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