2020 AMC 8 Problems/Problem 13

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 $\frac{18+9}{36+9}=\frac{27}{45}=\frac{3}{5}$ . ~icematrix

2020 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
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2020 AMC 8 Problems/Problem 13

Solution 1

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