Difference between revisions of "2020 AMC 8 Problems/Problem 13"
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==Solution 1== | ==Solution 1== | ||
− | After | + | After Jamal adds <math>x</math> purple socks, he has <math>18+x</math> purple socks and <math>6+18+12+x=x+36</math> total socks, for a probability of drawing a purple sock of <cmath>\dfrac{18+x}{36+x}=\dfrac{3}{5}.</cmath> Since <math>\dfrac{18+9}{36+9}=\dfrac{27}{45}=\dfrac35</math>, the answer is <math>\boxed{\textbf{(B) }9}</math>. ~icematrix |
==Solution 2== | ==Solution 2== |
Revision as of 19:04, 19 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 Jamal adds purple socks, he has purple socks and total socks, for a probability of drawing a purple sock of Since , the answer is . ~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
Video Solution
~savannahsolver
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 |
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