2020 AMC 8 Problems/Problem 13
Revision as of 08:57, 20 November 2020 by Sevenoptimus (talk | contribs) (Removed duplicates of essentially the same solution, and improved grammar and clarity)
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?
Solution 1
After Jamal adds purple socks, he has
purple socks and
total socks. This means the probability of drawing a purple sock is
, so we obtain
Since
, the answer is
.
Solution 2 (variant of Solution 1)
As in Solution 1, we have the equation . Cross-multiplying yields
. Thus, Jamal added
purple socks.
Video Solution
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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All AJHSME/AMC 8 Problems and Solutions |
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