2020 AMC 8

Complete problem set with solutions and individual problem pages

Problem 13 Medium

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?

  • A.

    6

  • B.

    9

  • C.

    12

  • D.

    18

  • E.

    24

Answer:B

Solution 1

After Jamal adds x purple socks, he has (18+x) purple socks and 6+18+12+x=(36+x) total socks. This means the probability of drawing a purple sock is \frac{18+x}{36+x}, so we obtain

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

Since \frac{18+9}{36+9}=\frac{27}{45}=\frac{3}{5}, the answer is \boxed{\textbf{(B) }9}.

 

Solution 2

6 green socks and 12 orange socks together should be 100\%-60\% = 40\% of the new total number of socks, so that new total must be \frac{6+12}{0.4}= 45. Therefore, 45-6-18-12=\boxed{\textbf{(B) }9} purple socks were added.

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