2020 AMC 8 Problems/Problem 15
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 .
Solution 5
of is 
, and of is 
. We put and into an equation, creating because equals . Solving for , dividing 
to both sides, we get , so the answer is .
Solution 6
of can be written as 
, or 
. of can similarly be written as 
, or 
. So now, 
. Using cross-multiplication, we can simplify the equation as: 
. Dividing both sides by 
, we get: 
. 
is the same thing as , so the answer is .
Video Solution
~savannahsolver
Video Solution
Video Solution by Interstigation
https://youtu.be/YnwkBZTv5Fw?t=665
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Video Solution (CLEVER MANIPULATIONS!!!)
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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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