Difference between revisions of "2024 AMC 8 Problems/Problem 21"

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==Problem==
 
==Problem==
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A group of frogs (called an army) is living in a tree. A frog turns green when in the shade and turns yellow
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when in the sun. Initially, the ratio of green to yellow frogs was <math>3 : 1</math>. Then <math>3</math> green frogs moved to the
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sunny side and <math>5</math> yellow frogs moved to the shady side. Now the ratio is <math>4 : 1</math>. What is the difference
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between the number of green frogs and the number of yellow frogs now?
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<math>\textbf{(A) } 10\qquad\textbf{(B) } 12\qquad\textbf{(C) } 16\qquad\textbf{(D) } 20\qquad\textbf{(E) } 24</math>
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==Solution 1==
 
==Solution 1==

Revision as of 14:04, 25 January 2024

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 $3 : 1$. Then $3$ green frogs moved to the sunny side and $5$ yellow frogs moved to the shady side. Now the ratio is $4 : 1$. What is the difference between the number of green frogs and the number of yellow frogs now?

$\textbf{(A) } 10\qquad\textbf{(B) } 12\qquad\textbf{(C) } 16\qquad\textbf{(D) } 20\qquad\textbf{(E) } 24$

Solution 1