2012 AMC 10B Problem 7

Question

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

Let the chipmunk dig

h

holes

Compare

3h

acorns with

4(h-4)

acorns

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 .

Problem 7 in other years