Difference between revisions of "2020 AMC 8 Problems/Problem 13"
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==Solution 3 (non-algebraic)== | ==Solution 3 (non-algebraic)== | ||
<math>6</math> green socks and <math>12</math> orange socks together should be <math>100\%-60\% = 40\%</math> of the new total number of socks, so that new total must be <math>\frac{6+12}{0.4}= 45</math>. Therefore, <math>45-6-18-12=\boxed{\textbf{(B) }9}</math> purple socks were added. | <math>6</math> green socks and <math>12</math> orange socks together should be <math>100\%-60\% = 40\%</math> of the new total number of socks, so that new total must be <math>\frac{6+12}{0.4}= 45</math>. Therefore, <math>45-6-18-12=\boxed{\textbf{(B) }9}</math> 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🚀)== | ||
| + | https://youtu.be/0nnyYRYi-40 | ||
| + | |||
| + | ~Education, the Study of Everything | ||
==Video Solution by North America Math Contest Go Go Go== | ==Video Solution by North America Math Contest Go Go Go== | ||
Latest revision as of 15:34, 26 January 2024
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 ![\[\frac{18+x}{36+x}=\frac{3}{5}\]](http://latex.artofproblemsolving.com/f/2/7/f27eeecf70d84202b3cd94eeb82151ab6f223b96.png)
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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
