AMC10 2012 B

AMC10 2012 B · Q7

AMC10 2012 B · Q7. It mainly tests Linear equations, Word problems (algebra).

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?

为了科学项目，Sammy 观察了一只花栗鼠和一只松鼠将橡子藏在洞里。花栗鼠在它挖的每个洞里藏了 3 个橡子。松鼠在它挖的每个洞里藏了 4 个橡子。它们各藏了相同数量的橡子，尽管松鼠用了少 4 个洞。花栗鼠藏了多少橡子？

(A) 30 30

(B) 36 36

(D) 48 48

(E) 54 54

Answer

Correct choice: (D)

正确答案：（D）

Solution

Let $h$ be the number of holes dug by the chipmunk. Then the\nchipmunk hid $3h$ acorns, while the squirrel hid $4(h - 4)$ acorns. Since they hid\nthe same number of acorns, $3h = 4(h - 4)$. Solving gives $h = 16$. Thus the\nchipmunk hid $3 \cdot 16 = 48$ acorns.

设 $h$ 为花栗鼠挖的洞数。那么花栗鼠藏了 $3h$ 个橡子，而松鼠藏了 $4(h - 4)$ 个橡子。由于它们藏了相同数量的橡子，$3h = 4(h - 4)$。解得 $h = 16$。因此花栗鼠藏了 $3 \cdot 16 = 48$ 个橡子。

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