Difference between revisions of "2020 AMC 8 Problems/Problem 15"
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− | + | ==Problem== | |
+ | Suppose <math>15\%</math> of <math>x</math> equals <math>20\%</math> of <math>y.</math> What percentage of <math>x</math> is <math>y?</math> | ||
+ | |||
+ | <math>\textbf{(A) }5 \qquad \textbf{(B) }35 \qquad \textbf{(C) }75 \qquad \textbf{(D) }133 \frac13 \qquad \textbf{(E) }300</math> | ||
==Solution 1== | ==Solution 1== | ||
− | + | Since <math>20\% = \frac{1}{5}</math>, multiplying the given condition by <math>5</math> shows that <math>y</math> is <math>15 \cdot 5 = \boxed{\textbf{(C) }75}</math> percent of <math>x</math>. | |
==Solution 2== | ==Solution 2== |
Revision as of 16:49, 19 December 2021
Contents
Problem
Suppose of equals of What percentage of is
Solution 1
Since , multiplying the given condition by shows that is percent of .
Solution 2
Letting (without loss of generality), the condition becomes . Clearly, it follows that is of , so the answer is .
Solution 3
We have and , so . Solving for , we multiply by to give , so the answer is .
Solution 4
We are given , so we may assume without loss of generality that and . This means , and thus the answer is .
Video Solution
~savannahsolver
Video Solution
Video Solution by Interstigation
https://youtu.be/YnwkBZTv5Fw?t=665
~Interstigation
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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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