2012 AMC 10A Problem 1

Below is the professionally curated solution for Problem 1 of the 2012 AMC 10A, 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.

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Concepts:rate unit conversion

Difficulty rating: 560

Cagney can frost a cupcake every $20$ seconds and Lacey can frost a cupcake every $30$ seconds. Working together, how many cupcakes can they frost in $5$ minutes?

$10$

$15$

$20$

$25$

$30$

Solution:

Cagney can make $60 \div 20 = 3$ cupcakes per minute, and Lacey can make $60 \div 30 = 2.$

In $5$ minutes, they can make $5(2 + 3) = 5 \cdot 5 = 25.$

Thus, D is the correct answer.

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