Difference between revisions of "2020 AMC 8 Problems/Problem 13"
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==Solution 1== | ==Solution 1== | ||
| − | After he adds <math>x</math> blue socks, the probability becomes <cmath>\frac{18+x}{6+18+12+x}\implies\frac{18+x}{36+x}=\frac{3}{5}.</cmath> Then, the answer is <math>\textbf{(B) }9</math> because <math>\frac{18+9}{ | + | After he adds <math>x</math> blue socks, the probability becomes <cmath>\frac{18+x}{6+18+12+x}\implies\frac{18+x}{36+x}=\frac{3}{5}.</cmath> Then, the answer is <math>\textbf{(B) }9</math> because <math>\frac{18+9}{36+9}=\frac{27}{45}=\frac{3}{5}</math>. ~icematrix |
| + | |||
| + | ==See also== | ||
| + | {{AMC8 box|year=2020|num-b=12|num-a=14}} | ||
| + | {{MAA Notice}} | ||
Revision as of 00:28, 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?
Solution 1
After he adds 
blue 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
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. 
