Question

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?

$6$

$9$

$12$

$18$

$24$

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Written solution:

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 Problem 13

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Written solution:

Problem 13 in Other Years