Jamal有个抽屉，里面有6只绿色袜子，18只紫色袜子，12只橙色袜子。当加了更多紫色袜子后，Jamal发现，从抽屉里随机抽取一只袜子，有60%的概率是紫色的。那么Jamal加了多少只紫色袜子？

A. 6

B. 9

C. 12

D. 18

E. 24

1. 2020 AMC 8 官方解析

A 60% chance of choosing a purple sock implies a 40% chance of choosing a green or orange sock. It follows that the $6 + 12 = 18$ non-purple socks represent 40% of all the socks. This means that 9 socks represent 20% of the total, and 27 socks represent 60% of the total. Jamal therefore added $27 - 18 = 9$ purple socks to the drawer.

随机选取一只袜子是紫色的概率为 60%，即随机取一只袜子是绿色袜子或橙色的袜子的概率为 40%. 因此，$6 + 12 = 18$ 只非紫色袜子占所有袜子的 40%. 则9只袜子占总数的20%，27只袜子占总数的 60%. 因此，Jamal 一共添加了 $27 - 18 = 9$ 只紫色袜子.

Let $x$ equal the number of additional purple socks, increasing the number of purple socks to $18 + x$ and the total number of socks to $36 + x$. Because the proportion of purple socks must equal 60%, the following equation must be satisfied:
$\frac{18 + x}{36 + x} = \frac{60}{100} = \frac{3}{5}$

Solving for $x$ yields
$5(18 + x) = 3(36 + x)$
$90 + 5x = 108 + 3x$
$2x = 18$
$x = 9.$

Jamal added 9 purple socks to the drawer.

假设$x$等于添加的紫色袜子的数量，则紫色袜子的数量增加到 $18 + x$，袜子的总数增加到 $36 + x$. 因为紫色袜子的比例必须等于60%，所以必须满足以下方程式：
$\frac{18 + x}{36 + x} = \frac{60}{100} = \frac{3}{5}$

求$x$的值：
$5(18 + x) = 3(36 + x)$
$90 + 5x = 108 + 3x$
$2x = 18$
$x = 9.$

因此Jamal 一共添加了 $27 - 18 = 9$ 只紫色袜子.