2020 AMC 8 Problems/Problem 13
Contents
Problem 13
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.
Solution 3 (non-algebraic)
green socks and
orange socks together should be
of the new total number of socks, so that new total must be
. It follows that
purple socks were added.
Video Solution
https://youtu.be/SPNobOd4t1c (Channel also has resources to prepare for your AIME qualification)
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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