2020 AMC 8 Problems/Problem 13
Contents
- 1 Problem 13
- 2 Solution 1
- 3 Solution 2 (variant of Solution 1)
- 4 Solution 3 (non-algebraic)
- 5 Video Solution by NiuniuMaths (Easy to understand!)
- 6 Video Solution by Math-X (First understand the problem!!!)
- 7 Video Solution (🚀Very Quick🚀)
- 8 Video Solution by North America Math Contest Go Go Go
- 9 Video Solution by WhyMath
- 10 Video Solution
- 11 Video Solution by Interstigation
- 12 See also
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 . Therefore, purple socks were added.
Video Solution by NiuniuMaths (Easy to understand!)
https://www.youtube.com/watch?v=bHNrBwwUCMI
~NiuniuMaths
Video Solution by Math-X (First understand the problem!!!)
https://youtu.be/UnVo6jZ3Wnk?si=6Ux3fNTMn5tSUnP3&t=1833
~Math-X
Video Solution (🚀Very Quick🚀)
~Education, the Study of Everything
Video Solution by North America Math Contest Go Go Go
https://www.youtube.com/watch?v=u81EWYcC0Wg
~North America Math Contest Go Go Go
Video Solution by WhyMath
~savannahsolver
Video Solution
Video Solution by Interstigation
https://youtu.be/YnwkBZTv5Fw?t=546
~Interstigation
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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