2012 AMC 10A Problems/Problem 1

Problem 1

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)
Preceded by First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

Page

Toolbox

Search

2012 AMC 10A Problems/Problem 1

Problem 1

Solution

See Also