2012 AMC 10B Problem 7

Below is the professionally curated solution for Problem 7 of the 2012 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 10B solutions, or check the answer key.

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Concepts:linear equation fraction

Difficulty rating: 1020

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?

$30$

$36$

$42$

$48$

$54$

Solution:

Let the number of acorns they each hid be $x.$ Then, the number of holes from the chipmunk is $\dfrac x3$ and the number of holes from the squirrel is $\dfrac x4 .$

This means $\dfrac x3 - \dfrac x4 = \dfrac{x}{12}= 4$ Therefore, $x=48.$

Thus, the correct answer is D .

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