Problem 5 · 2010 AMC 8
Easy
Arithmetic & Operations
unit-conversion
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?
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Answer: B — 34 cm.
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Hint 1 of 2
Everything stacks up to the same total height. From the floor: stool + Alice + her reach must equal the height of the bulb. The stool is the only missing piece.
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Hint 2 of 2
First make every measurement use the same unit — mixing meters and centimeters is the classic trap here. Turn the meters into centimeters before you add anything.
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Approach: stack the heights, convert units first
- Convert to centimeters so nothing is mismatched: ceiling 240, Alice 150. The bulb hangs 10 below the ceiling, so it's at 240 − 10 = 230 cm.
- Standing on the stool, Alice reaches stool + 150 + 46 = stool + 196. That just touches the bulb at 230.
- Stool = 230 − 196 = 34 cm.
- Why this transfers: in any ‘how tall / how far’ word problem, your very first move is to put all lengths in one unit. The numbers 2.4 m and 150 cm look ready to subtract — they aren't.
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