Difference between revisions of "2020 AMC 8 Problems/Problem 13"
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==Solution 2== | ==Solution 2== | ||
The total number of socks that Jamal has is <math>\, 6+18+12=36</math> socks. We are trying to determine how many purple socks he added to his drawer. Let's say he adds <math>x</math> purple socks. This means that the total number of purple socks in his drawer will be <math>(18+x)</math> and the new total number of socks in his drawer will be <math>(36+x)</math>. The ratio of purple socks to total socks in his drawer is now <math>\frac{60}{100}=\frac{3}{5}</math>. This leads to the equation <math>\frac{18+x}{36+x}=\frac{3}{5}</math>. Cross multiplying this equation gives us <math>90+5x=108+3x \implies 2x=18 \implies x=9</math>. Thus, Jamal added 9 purple socks <math>\implies\boxed{\textbf{(B) }9}</math>.<br> | The total number of socks that Jamal has is <math>\, 6+18+12=36</math> socks. We are trying to determine how many purple socks he added to his drawer. Let's say he adds <math>x</math> purple socks. This means that the total number of purple socks in his drawer will be <math>(18+x)</math> and the new total number of socks in his drawer will be <math>(36+x)</math>. The ratio of purple socks to total socks in his drawer is now <math>\frac{60}{100}=\frac{3}{5}</math>. This leads to the equation <math>\frac{18+x}{36+x}=\frac{3}{5}</math>. Cross multiplying this equation gives us <math>90+5x=108+3x \implies 2x=18 \implies x=9</math>. Thus, Jamal added 9 purple socks <math>\implies\boxed{\textbf{(B) }9}</math>.<br> | ||
| − | ~ junaidmansuri | + | ~[http://artofproblemsolving.com/community/user/jmansuri junaidmansuri] |
| + | |||
==Solution 3== | ==Solution 3== | ||
Revision as of 18:35, 18 November 2020
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?
Contents
Solution 1
After he adds 
purple socks, the probability becomes ![\[\frac{18+x}{6+18+12+x}\implies\frac{18+x}{36+x}=\frac{3}{5}.\]](http://latex.artofproblemsolving.com/8/4/6/8466c155611eb9d6984aeec00f9ff7e1d1197afd.png)
Then, the answer is 
because 
. ~icematrix
Solution 2
The total number of socks that Jamal has is 
socks. We are trying to determine how many purple socks he added to his drawer. Let's say he adds purple socks. This means that the total number of purple socks in his drawer will be 
and the new total number of socks in his drawer will be 
. The ratio of purple socks to total socks in his drawer is now 
. This leads to the equation 
. Cross multiplying this equation gives us 
. Thus, Jamal added 9 purple socks 
.
~junaidmansuri
Solution 3
Let Jamal add more purple socks. Then we are told that 
. Cross multiplying and simplifying tells us that 
.
-franzliszt
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. 
