Problem:
Jamal has a drawer containing green socks, purple socks, and orange socks. After adding more purple socks, Jamal noticed that there is now a chance that a sock randomly selected from the drawer is purple. How many purple socks did Jamal add?
Answer Choices:
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E.
Solution:
Suppose Jamal adds purple socks. Then, there will be purple socks. Also, since there are total socks to begin with, we have socks after adding the socks. Since we have a chance of choosing a purple sock afterwards, we know
Solving for :
Therefore, socks are added.
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions