AMC 8 2020 Problem 13 | Probability Problem

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

AMC 8 2020 Problem 13

9

At first Let Jamal adds $x$ purple socks,

So, He have $18+x$ purple Socks now, in total He has $36+x$

So probability of drawing a purple sock is $\frac{18+x}{36+x}$

Hence,

$\frac{18+x}{36+x}=\frac{3}{5}$

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