2012 AMC 10A Problem 1

Attempt Problem 1 of the 2012 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 2012 AMC 10A solutions, or check the answer key.

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

1.

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 each frosting rate to cupcakes per minute
Big hint:
Add the two rates, then multiply by 55 minutes
Solution:
Cagney can make 60÷20=360 \div 20 = 3 cupcakes per minute, and Lacey can make 60÷30=2.60 \div 30 = 2.
In 55 minutes, they can make 5(2+3)=5⋅5=25. 5(2 + 3) = 5 \cdot 5 = 25.
Thus, D is the correct answer.
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