Difference between revisions of "2020 AMC 8 Problems/Problem 13"
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Sevenoptimus (talk | contribs) (Cleaned up Solution 3) |
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As in Solution 1, we have the equation <math>\frac{18+x}{36+x}=\frac{3}{5}</math>. Cross-multiplying yields <math>90+5x=108+3x \Rightarrow 2x=18 \Rightarrow x=9</math>. Thus, Jamal added <math>\boxed{\textbf{(B) }9}</math> purple socks. | As in Solution 1, we have the equation <math>\frac{18+x}{36+x}=\frac{3}{5}</math>. Cross-multiplying yields <math>90+5x=108+3x \Rightarrow 2x=18 \Rightarrow x=9</math>. Thus, Jamal added <math>\boxed{\textbf{(B) }9}</math> purple socks. | ||
− | ==Solution 3 ( | + | ==Solution 3 (non-algebraic)== |
− | <math>6</math> green socks and <math>12</math> orange socks together | + | <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>. It follows that <math>45-6-18-12=\boxed{\textbf{(B) }9}</math> purple socks were added. |
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==Video Solution== | ==Video Solution== |
Revision as of 22:38, 20 November 2020
Contents
Problem
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 . It follows that purple socks were added.
Video Solution
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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