2024 AMC 8 Problem 21
Attempt Problem 21 of the 2024 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
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 yellow frogs now?
Answer: E
Small hint:
Let the initial yellow count be
Big hint:
After the moves, green changes by and yellow changes by
Video solution:
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Written solution:
We can let be the number of green frogs and be the number of yellow frogs. Initially, we have . Then, after some frogs moved, we have the following proportion:
Substituting for will allow us to determine the number of yellow frogs originally ():
Hence, there were yellow frogs and green frogs initially. After some frogs moved, we now have yellow frogs and green frogs, giving us a difference of between the number of green and yellow frogs.
Thus, E is the correct answer.
Problem 21 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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- 1998 AMC 8
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