AMC8 2010

AMC8 2010 · Q5

AMC8 2010 · Q5. It mainly tests Unit conversion, Arithmetic misc.

Alice needs to replace a light bulb located 10 centimeters below the ceiling in her kitchen. The ceiling is 2.4 meters above the floor. Alice is 1.5 meters tall and can reach 46 centimeters above the top of her head. Standing on a stool, she can just reach the light bulb. What is the height of the stool, in centimeters?

Alice需要更换厨房天花板下方10厘米处的灯泡。天花板离地面2.4米。Alice身高1.5米，伸直手臂可达头顶上方46厘米。站在凳子上，她刚好能碰到灯泡。凳子的高度是多少厘米？

(A) 32 32

(B) 34 34

(D) 38 38

(E) 40 40

Answer

Correct choice: (B)

正确答案：（B）

Solution

Convert everything to the same unit. Since the answer is in centimeters, change meters to centimeters by moving the decimal place two places to the right. The ceiling is $240$ centimeters above the floor. The combined height of Alice and the light bulb when she reaches for it is $10+150+46=206$ centimeters. That means the stool's height needs to be $240-206=\boxed{\textbf{(B)}\ 34}$

将所有单位转换为厘米，将米的小数点向右移两位。天花板离地面$240$厘米。Alice身高加伸手可达灯泡的高度为$10+150+46=206$厘米。因此，凳子高度需要为$240-206=\boxed{\textbf{(B)}\ 34}$

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