2012 AMC 12A Problem 2

Attempt Problem 2 of the 2012 AMC 12A 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 2012 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

2.

Cagney can frost a cupcake every 2020 seconds and Lacey can frost a cupcake every 3030 seconds. Working together, how many cupcakes can they frost in 55 minutes?
1010
1515
2020
2525
3030
Answer: D
Concepts:rateunit conversion
Small hint:
Convert 55 minutes to seconds, or count each person’s cupcakes per minute
Big hint:
In 55 minutes Cagney frosts 30020\dfrac{300}{20} and Lacey frosts 30030\dfrac{300}{30}
Solution:
In 55 minutes there are 300300 seconds. Cagney frosts 30020=15\dfrac{300}{20} = 15 cupcakes and Lacey frosts 30030=10\dfrac{300}{30} = 10 cupcakes.
Together they frost 15+10=2515 + 10 = 25 cupcakes.
Thus, the correct answer is D.
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