AMC 8 2010 Problem 5
AMC8 2010 年第 5 题
表达式与运算★★☆☆☆
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 需要换掉厨房的一个灯泡，灯泡位于天花板下面 10 厘米，天花板离地面 2.4 米。
Alice 有 1.5 米高，并且可以碰到离她头顶 46 厘米高的地方。当她站在凳子上，她恰好可以碰到灯泡。那么凳子的高度是多少厘米？
- A.32
- B.34
- C.36
- D.38
- E.40
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
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=34
Convert everything to the same unit. Since the answer is in centimeters, change meters to centimeters by multiplying by 100. So, the ceiling is 240 centimeters above the floor. 10 cm below means the light is at 230 cm. Because Alice is 150 cm, and she can reach 46 cm above her head, her reach height is 46+150=196. The height of the stool is the difference of the heights; 230-196=34 cm. -N. Video by MathTalks https:
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