Problem 11 · 2017 Math Kangaroo
Medium
Algebra & Patterns
substitution
A furniture shop sells 3-seater, 2-seater and 1-seater sofas. Each sofa has an equally wide armrest on the left and on the right, and every seat is equally wide (see picture). With its armrests the 3-seater sofa is 220 cm wide and the 2-seater sofa is 160 cm wide. How wide is the 1-seater sofa?
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Answer: D — 100 cm
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Hint 1 of 2
Both sofas have two armrests; the only difference between the 3-seater and 2-seater is one seat.
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Hint 2 of 2
Find one seat's width from the 220 vs 160 difference, then build the 1-seater.
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Approach: subtract to isolate a seat, then a pair of armrests
- 3-seater: 3 seats + 2 armrests = 220; 2-seater: 2 seats + 2 armrests = 160.
- Subtracting, one seat = 220 − 160 = 60 cm.
- From the 2-seater, 2 armrests = 160 − 2×60 = 40 cm.
- The 1-seater = 1 seat + 2 armrests = 60 + 40 = 100 cm (D).
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