Difference between revisions of "2024 AMC 8 Problems/Problem 21"
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− | 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 <math>(B)</math> and <math>(E)</math>. | + | Since the original ratio is <math>3:1</math> and the new ratio is <math>4:1</math>, the number of frogs must be a multiple of <math>12</math>, the only solutions left are <math>(B)</math> and <math>(E)</math>. |
Let's start with <math>12</math>. If the starting difference is <math>3x:x</math>. | Let's start with <math>12</math>. If the starting difference is <math>3x:x</math>. |
Revision as of 17:22, 26 January 2024
Contents
[hide]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 and the new ratio is , the number of frogs must be a multiple of , the only solutions left are and .
Let's start with . If the starting difference is .
Using the starting ratio, there are 9 green frogs and three yellow. Afterwards there are 11 green frogs and 1 yellow, this doesn't work
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