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2012 AMC 10B Problems/Problem 7

Revision as of 11:41, 24 February 2012 by Iggy Iguana (talk | contribs) (Solutions)

Problem 7

For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chipmunk hide?

$\textbf{(A)}\ 30\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 42\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 54$


Solutions

Let $x$ be the number of acorns that both animals had.

So by the info in the problem:

$\frac{x}{3}=(\frac{x}{4})+4$ $\frac{x}{12}=4$ $\boxed{x=48}$

This is answer choice $\textbf{(D)}$

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