Problem 1 · 2015 AMC 8
Easy
Geometry & Measurement
areaunit-rate
How many square yards of carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide? (There are 3 feet in a yard.)
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Answer: A — 12 square yards.
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Hint 1 of 2
The trap is to find the area in square feet (12 × 9 = 108) and then divide by 3. But a square yard isn't 3 square feet — it's a 3-by-3 block, which is 9 square feet. Convert the lengths first, then there's nothing to undo.
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Hint 2 of 2
Convert each side to yards before multiplying. (General rule: change units on lengths first, then compute area or volume — never convert the answer.)
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Approach: convert the side lengths to yards first, then multiply
- Convert the lengths, not the area: 12 ft = 4 yd and 9 ft = 3 yd.
- Area = 4 yd × 3 yd = 12 square yards.
- Why this transfers: area and volume scale by the square (or cube) of a length conversion. 1 yd = 3 ft, so 1 sq yd = 32 = 9 sq ft — which is exactly why 108 sq ft ÷ 9 = 12 sq yd also works, and matches our answer. Converting lengths first dodges that factor entirely.
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