2012 AMC 10A Problems/Problem 1

The following problem is from both the 2012 AMC 12A #2 and 2012 AMC 10A #1, so both problems redirect to this page.

Problem

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?

$\textbf{(A)}\ 10\qquad\textbf{(B)}\ 15\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 25\qquad\textbf{(E)}\ 30$

Solution

Cagney can frost one in 20 seconds, and Lacey can frost one in 30 seconds. Working together, they can frost one in $\frac{20*30}{20+30} = \frac{600}{50} = 12$ seconds. In 300 seconds (5 minutes), they can frost $\boxed{\textbf{(D)}\ 25 \text{ cupcakes }}$ .

2012 AMC 10A (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

2012 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

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2012 AMC 10A Problems/Problem 1

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