2010 AMC 10A Problem 3
Attempt Problem 3 of the 2010 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2010 AMC 10A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
3.
Tyrone had marbles and Eric had marbles. Tyrone then gave some of his marbles to Eric so that Tyrone ended with twice as many marbles as Eric. How many marbles did Tyrone give to Eric?
Answer: D
Small hint:
The total number of marbles stays fixed
Big hint:
The final amounts are in the ratio
Solution:
Let be the number of marbles that Eric ends up with. Then Tyrone ends up with
The total number of marbles is so
Then, Tyrone ends up with marbles. This means he has to give away marbles.
Thus, D is the correct answer.
Problem 3 in other years
- 2000 AMC 10
- 2001 AMC 10
- 2002 AMC 10A
- 2002 AMC 10B
- 2003 AMC 10A
- 2003 AMC 10B
- 2004 AMC 10A
- 2004 AMC 10B
- 2005 AMC 10A
- 2005 AMC 10B
- 2006 AMC 10A
- 2006 AMC 10B
- 2007 AMC 10A
- 2007 AMC 10B
- 2008 AMC 10A
- 2008 AMC 10B
- 2009 AMC 10A
- 2009 AMC 10B
- 2010 AMC 10B
- 2011 AMC 10A
- 2011 AMC 10B
- 2012 AMC 10A
- 2012 AMC 10B
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- 2013 AMC 10B
- 2014 AMC 10A
- 2014 AMC 10B
- 2015 AMC 10A
- 2015 AMC 10B
- 2016 AMC 10A
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- 2017 AMC 10B
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- 2018 AMC 10B
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- 2019 AMC 10B
- 2020 AMC 10A
- 2020 AMC 10B
- 2021 AMC 10A Spring
- 2021 AMC 10B Spring
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- 2021 AMC 10B Fall
- 2022 AMC 10A
- 2022 AMC 10B
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- 2023 AMC 10B
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- 2025 AMC 10B