Difference between revisions of "2024 AMC 8 Problems/Problem 21"
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==Video Solution 3 by SpreadTheMathLove== | ==Video Solution 3 by SpreadTheMathLove== | ||
https://www.youtube.com/watch?v=3ItvjukLqK0 | https://www.youtube.com/watch?v=3ItvjukLqK0 | ||
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| + | == Video Solution by CosineMethod [🔥Fast and Easy🔥]== | ||
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| + | https://www.youtube.com/watch?v=3SUTUr1My7c&t=1s | ||
Revision as of 14:45, 26 January 2024
Contents
Problem
A group of frogs (called an army) is living in a tree. A frog turns green when in the shade and turns yellow
when in the sun. Initially, the ratio of green to yellow frogs was 
. Then 
green frogs moved to the
sunny side and 
yellow frogs moved to the shady side. Now the ratio is 
. What is the difference
between the number of green frogs and the number of yellow frogs now?
Solution 1
Let the initial number of green frogs be 
and the initial number of yellow frogs be 
. Since the ratio of the number of green frogs to yellow frogs is initially , 
. Now, green frogs move to the sunny side and yellow frogs move to the shade side, thus the new number of green frogs is 
and the new number of yellow frogs is 
. We are given that 
, so 
, since , we have 
, so 
and 
. Thus the answer is 
.
Solution 2
Since the original ratio is 3:1 and the new ratio is 4:1, the number of frogs must be a multiple of 12, the only solutions left are 
and 
.
Let's start with 
. If the starting difference is 
, then the difference after the move is 
.
If you solve, x isn't an integer.
Therefore the answer must be 
.
Video Solution 1 by Math-X (First fully understand the problem!!!)
https://www.youtube.com/watch?v=zBe5vrQbn2A
~Math-X
Video Solution 2 by OmegaLearn.org
Video Solution 3 by SpreadTheMathLove
https://www.youtube.com/watch?v=3ItvjukLqK0
