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2020 AMC 8 Problems/Problem 13

Revision as of 00:27, 18 November 2020 by Icematrix2 (talk | contribs) (Created page with "Jamal has a drawer containing <math>6</math> green socks, <math>18</math> purple socks, and <math>12</math> orange socks. After adding more purple socks, Jamal noticed that th...")
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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?

$\textbf{(A) }6 \qquad \textbf{(B) }9 \qquad \textbf{(C) }12 \qquad \textbf{(D) }18 \qquad \textbf{(E) }24$

Solution 1

After he adds $x$ blue socks, the probability becomes \[\frac{18+x}{6+18+12+x}\implies\frac{18+x}{36+x}=\frac{3}{5}.\] Then, the answer is $\textbf{(B) }9$ because $\frac{18+9}{26+9}=\frac{27}{45}=\frac{3}{5}$. ~icematrix

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